{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from IPython.display import YouTubeVideo\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multidimensional Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## for a Constant Acceleration Model (CA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Situation covered: You have a Position Sensor (e.g. a Vision System) and try to calculate velocity ($\\dot x$ and $\\dot y$) as well as position ($x$ and $y$) of a ball in 3D space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/tIIJME8-au8\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x103e7bfd0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo(\"tIIJME8-au8\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State Vector - Constant Acceleration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Constant Acceleration Model for Motion in 3D\n",
    "\n",
    "$$x= \\left[ \\matrix{ x \\\\ y \\\\ z \\\\ \\dot x \\\\ \\dot y \\\\ \\dot z \\\\ \\ddot x \\\\ \\ddot y \\\\ \\ddot z} \\right]$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Formal Definition:\n",
    "\n",
    "$$x_{k+1} = A \\cdot x_{k} + B \\cdot u_k$$\n",
    "\n",
    "Hence, we have no control input $u$.\n",
    "\n",
    "$$x_{k+1} = \\begin{bmatrix}1 & 0 & 0 & \\Delta t & 0 & 0 & \\frac{1}{2}\\Delta t^2 & 0 & 0 \\\\ 0 & 1 & 0 & 0 & \\Delta t & 0 & 0 & \\frac{1}{2}\\Delta t^2 & 0 \\\\ 0 & 0 & 1 & 0 & 0 & \\Delta t & 0 & 0 & \\frac{1}{2}\\Delta t^2 \\\\ 0 & 0 & 0 & 1 & 0 & 0 & \\Delta t & 0 & 0 \\\\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & \\Delta t & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & \\Delta t \\\\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\end{bmatrix} \\cdot \\begin{bmatrix} x \\\\ y \\\\ z \\\\ \\dot x \\\\ \\dot y \\\\ \\dot z \\\\ \\ddot x \\\\ \\ddot y \\\\ \\ddot z\\end{bmatrix}_{k}$$\n",
    "\n",
    "$$y = H \\cdot x$$\n",
    "\n",
    "Position ($x$ & $y$ & $z$) is measured with vision system:\n",
    "\n",
    "$$y = \\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\end{bmatrix} \\cdot x$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Initial Uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/paul/anaconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
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WEWWroJygzMwqwgnKzMwKqWwJyn1QZmZWSK6gzMwqomwVlBOUmVlFOEGZmVkhlS1BuQ/K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\nKEqBS0SISwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b6ef90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = 100.0*np.eye(9)\n",
    "\n",
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Initial Covariance Matrix $P$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(10))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,8.5])\n",
    "plt.ylim([8.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9, 9)\n"
     ]
    }
   ],
   "source": [
    "dt = 0.01 # Time Step between Filter Steps\n",
    "\n",
    "A = np.matrix([[1.0, 0.0, 0.0, dt, 0.0, 0.0, 1/2.0*dt**2, 0.0, 0.0],\n",
    "              [0.0, 1.0, 0.0, 0.0,  dt, 0.0, 0.0, 1/2.0*dt**2, 0.0],\n",
    "              [0.0, 0.0, 1.0, 0.0, 0.0,  dt, 0.0, 0.0, 1/2.0*dt**2],\n",
    "              [0.0, 0.0, 0.0, 1.0, 0.0, 0.0,  dt, 0.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0,  dt, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0,  dt],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "print(A.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurement Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here you can determine, which of the states is covered by a measurement. In this example, the position ($x$ and $y$) is measured."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
      "        [ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
      "        [ 0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.]]), (3, 9))\n"
     ]
    }
   ],
   "source": [
    "H = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "               [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "               [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]])\n",
    "print(H, H.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurement Noise Covariance Matrix $R$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 1.,  0.,  0.],\n",
      "        [ 0.,  1.,  0.],\n",
      "        [ 0.,  0.,  1.]]), (3, 3))\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b6e190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rp = 1.0**2  # Noise of Position Measurement\n",
    "R = np.matrix([[rp, 0.0, 0.0],\n",
    "               [0.0, rp, 0.0],\n",
    "               [0.0, 0.0, rp]])\n",
    "print(R, R.shape)\n",
    "\n",
    "fig = plt.figure(figsize=(4, 4))\n",
    "im = plt.imshow(R, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Measurement Noise Covariance Matrix $R$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(4))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(3),('$x$', '$y$', '$z$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(4))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(3),('$x$', '$y$', '$z$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,2.5])\n",
    "plt.ylim([2.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Process Noise Covariance Matrix $Q$ for CA Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Position of the ball can be influenced by a force (e.g. wind), which leads to an acceleration disturbance (noise). This process noise has to be modeled with the process noise covariance matrix Q.\n",
    "\n",
    "To easily calcualte Q, one can ask the question: How the noise effects my state vector? For example, how the acceleration change the position over one timestep dt.\n",
    "\n",
    "One can calculate Q as\n",
    "\n",
    "$$Q = G\\cdot G^T \\cdot \\sigma_a^2$$\n",
    "\n",
    "with $G = \\begin{bmatrix}0.5dt^2 & 0.5dt^2 & 0.5dt^2 & dt & dt & dt & 1.0 &1.0 & 1.0\\end{bmatrix}^T$ and $\\sigma_a$ as the acceleration process noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Symbolic Calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0 & 1.0\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0 & 1.0\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0 & 1.0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡             4               4               4              3              3 \n",
       "⎢0.25⋅\\Delta t   0.25⋅\\Delta t   0.25⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t  \n",
       "⎢                                                                             \n",
       "⎢             4               4               4              3              3 \n",
       "⎢0.25⋅\\Delta t   0.25⋅\\Delta t   0.25⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t  \n",
       "⎢                                                                             \n",
       "⎢             4               4               4              3              3 \n",
       "⎢0.25⋅\\Delta t   0.25⋅\\Delta t   0.25⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t  \n",
       "⎢                                                                             \n",
       "⎢            3               3               3             2              2   \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t    0.5⋅\\Delta t      \\Delta t       \\Delta t    \n",
       "⎢                                                                             \n",
       "⎢            3               3               3             2              2   \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t    0.5⋅\\Delta t      \\Delta t       \\Delta t    \n",
       "⎢                                                                             \n",
       "⎢            3               3               3             2              2   \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t    0.5⋅\\Delta t      \\Delta t       \\Delta t    \n",
       "⎢                                                                             \n",
       "⎢            2               2               2                                \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t    0.5⋅\\Delta t    1.0⋅\\Delta t   1.0⋅\\Delta t  \n",
       "⎢                                                                             \n",
       "⎢            2               2               2                                \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t    0.5⋅\\Delta t    1.0⋅\\Delta t   1.0⋅\\Delta t  \n",
       "⎢                                                                             \n",
       "⎢            2               2               2                                \n",
       "⎣0.5⋅\\Delta t    0.5⋅\\Delta t    0.5⋅\\Delta t    1.0⋅\\Delta t   1.0⋅\\Delta t  \n",
       "\n",
       "             3              2              2              2⎤\n",
       " 0.5⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t ⎥\n",
       "                                                           ⎥\n",
       "             3              2              2              2⎥\n",
       " 0.5⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t ⎥\n",
       "                                                           ⎥\n",
       "             3              2              2              2⎥\n",
       " 0.5⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t ⎥\n",
       "                                                           ⎥\n",
       "           2                                               ⎥\n",
       "   \\Delta t     1.0⋅\\Delta t   1.0⋅\\Delta t   1.0⋅\\Delta t ⎥\n",
       "                                                           ⎥\n",
       "           2                                               ⎥\n",
       "   \\Delta t     1.0⋅\\Delta t   1.0⋅\\Delta t   1.0⋅\\Delta t ⎥\n",
       "                                                           ⎥\n",
       "           2                                               ⎥\n",
       "   \\Delta t     1.0⋅\\Delta t   1.0⋅\\Delta t   1.0⋅\\Delta t ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       " 1.0⋅\\Delta t        1.0            1.0            1.0     ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       " 1.0⋅\\Delta t        1.0            1.0            1.0     ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       " 1.0⋅\\Delta t        1.0            1.0            1.0     ⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Symbol, Matrix\n",
    "from sympy.interactive import printing\n",
    "printing.init_printing()\n",
    "dts = Symbol('\\Delta t')\n",
    "Qs = Matrix([[0.5*dts**2],[0.5*dts**2],[0.5*dts**2],[dts],[dts],[dts],[1.0],[1.0],[1.0]])\n",
    "Qs*Qs.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9, 9)\n"
     ]
    }
   ],
   "source": [
    "sa = 0.1\n",
    "G = np.matrix([[1/2.0*dt**2],\n",
    "               [1/2.0*dt**2],\n",
    "               [1/2.0*dt**2],\n",
    "               [dt],\n",
    "               [dt],\n",
    "               [dt],\n",
    "               [1.0],\n",
    "               [1.0],\n",
    "               [1.0]])\n",
    "Q = G*G.T*sa**2\n",
    "\n",
    "print(Q.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ewJWNDMrMzPLr1ASV+xSfpOXAA5LGpulRwKeBqyLCN+iambWIpCG9iqqea1CHATcDj0vq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10822a750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Process Noise Covariance Matrix $Q$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(10))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,8.5])\n",
    "plt.ylim([8.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Disturbance Control Matrix $B$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.]]), (9, 1))\n"
     ]
    }
   ],
   "source": [
    "B = np.matrix([[0.0],\n",
    "               [0.0],\n",
    "               [0.0],\n",
    "               [0.0],\n",
    "               [0.0],\n",
    "               [0.0],\n",
    "               [0.0],\n",
    "               [0.0],\n",
    "               [0.0]])\n",
    "print(B, B.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Control Input $u$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assumed constant over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "u = 0.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Identity Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.]]), (9, 9))\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(9)\n",
    "print(I, I.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Synthetically creation of the Position Data for the ball"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Hz = 100.0 # Frequency of Vision System\n",
    "dt = 1.0/Hz\n",
    "T = 1.0 # s measuremnt time\n",
    "m = int(T/dt) # number of measurements\n",
    "\n",
    "px= 0.0 # x Position Start\n",
    "py= 0.0 # y Position Start\n",
    "pz= 1.0 # z Position Start\n",
    "\n",
    "vx = 10.0 # m/s Velocity at the beginning\n",
    "vy = 0.0 # m/s Velocity\n",
    "vz = 0.0 # m/s Velocity\n",
    "\n",
    "c = 0.1 # Drag Resistance Coefficient\n",
    "d = 0.9 # Damping\n",
    "\n",
    "Xr=[]\n",
    "Yr=[]\n",
    "Zr=[]\n",
    "for i in range(int(m)):\n",
    "    accx = -c*vx**2  # Drag Resistance\n",
    "    \n",
    "    vx += accx*dt\n",
    "    px += vx*dt\n",
    "\n",
    "    accz = -9.806 + c*vz**2 # Gravitation + Drag\n",
    "    vz += accz*dt\n",
    "    pz += vz*dt\n",
    "    \n",
    "    if pz<0.01:\n",
    "        vz=-vz*d\n",
    "        pz+=0.02\n",
    "    if vx<0.1:\n",
    "        accx=0.0\n",
    "        accz=0.0\n",
    "        \n",
    "    Xr.append(px)\n",
    "    Yr.append(py)\n",
    "    Zr.append(pz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Add Noise to the Real Position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sp= 0.1 # Sigma for position noise\n",
    "\n",
    "Xm = Xr + sp * (np.random.randn(m))\n",
    "Ym = Yr + sp * (np.random.randn(m))\n",
    "Zm = Zr + sp * (np.random.randn(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATsAAAAWCAYAAAC/mTubAAAABHNCSVQICAgIfAhkiAAACJNJREFU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\n",
      "text/latex": [
       "$$\\left ( -1.68366184104, \\quad 2.89434972763\\right )$$"
      ],
      "text/plain": [
       "(-1.68366184104, 2.89434972763)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4PMqNounTp4vbb79dHDp0KOH1Un2e0x3Pe/fuVbZBtvs42d13390hDE+bNk0sX75cbNiw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/992O123Hnnnbj33nvDGuvixYtsXqJarUaHDh1w6dKlK36OT5sP5u8XX3wRH330EXbt2oWOHTvi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\n/g/u9YfeniJeJwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108252510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.scatter(Xm, Ym, Zm, c='gray')\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "plt.title('Ball Trajectory observed from Computer Vision System (with Noise)')\n",
    "\n",
    "#ax.w_xaxis.set_pane_color((1.0, 1.0, 1.0, 1.0))\n",
    "\n",
    "# Axis equal\n",
    "max_range = np.array([Xm.max()-Xm.min(), Ym.max()-Ym.min(), Zm.max()-Zm.min()]).max() / 3.0\n",
    "mean_x = Xm.mean()\n",
    "mean_y = Ym.mean()\n",
    "mean_z = Zm.mean()\n",
    "ax.set_xlim(mean_x - max_range, mean_x + max_range)\n",
    "ax.set_ylim(mean_y - max_range, mean_y + max_range)\n",
    "ax.set_zlim(mean_z - max_range, mean_z + max_range)\n",
    "#plt.savefig('BallTrajectory-Computervision.png', dpi=150, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 100)\n"
     ]
    }
   ],
   "source": [
    "measurements = np.vstack((Xm,Ym,Zm))\n",
    "print(measurements.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Initial State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[  0.  ],\n",
      "        [  0.  ],\n",
      "        [  1.  ],\n",
      "        [ 10.  ],\n",
      "        [  0.  ],\n",
      "        [  0.  ],\n",
      "        [  0.  ],\n",
      "        [  0.  ],\n",
      "        [ -9.81]]), (9, 1))\n"
     ]
    }
   ],
   "source": [
    "x = np.matrix([0.0, 0.0, 1.0, 10.0, 0.0, 0.0, 0.0, 0.0, -9.81]).T\n",
    "print(x, x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Preallocation for Plotting\n",
    "xt = []\n",
    "yt = []\n",
    "zt = []\n",
    "dxt= []\n",
    "dyt= []\n",
    "dzt= []\n",
    "ddxt=[]\n",
    "ddyt=[]\n",
    "ddzt=[]\n",
    "Zx = []\n",
    "Zy = []\n",
    "Zz = []\n",
    "Px = []\n",
    "Py = []\n",
    "Pz = []\n",
    "Pdx= []\n",
    "Pdy= []\n",
    "Pdz= []\n",
    "Pddx=[]\n",
    "Pddy=[]\n",
    "Pddz=[]\n",
    "Kx = []\n",
    "Ky = []\n",
    "Kz = []\n",
    "Kdx= []\n",
    "Kdy= []\n",
    "Kdz= []\n",
    "Kddx=[]\n",
    "Kddy=[]\n",
    "Kddz=[]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Kalman Filter](Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "hitplate=False\n",
    "for filterstep in range(m):\n",
    "    \n",
    "    # Model the direction switch, when hitting the plate\n",
    "    if x[2]<0.01 and not hitplate:\n",
    "        x[5]=-x[5]\n",
    "        hitplate=True\n",
    "    \n",
    "    # Time Update (Prediction)\n",
    "    # ========================\n",
    "    # Project the state ahead\n",
    "    x = A*x + B*u\n",
    "    \n",
    "    # Project the error covariance ahead\n",
    "    P = A*P*A.T + Q    \n",
    "    \n",
    "    \n",
    "    # Measurement Update (Correction)\n",
    "    # ===============================\n",
    "    # Compute the Kalman Gain\n",
    "    S = H*P*H.T + R\n",
    "    K = (P*H.T) * np.linalg.pinv(S)\n",
    "\n",
    "    \n",
    "    # Update the estimate via z\n",
    "    Z = measurements[:,filterstep].reshape(H.shape[0],1)\n",
    "    y = Z - (H*x)                            # Innovation or Residual\n",
    "    x = x + (K*y)\n",
    "    \n",
    "    # Update the error covariance\n",
    "    P = (I - (K*H))*P\n",
    "    \n",
    "   \n",
    "    \n",
    "    # Save states for Plotting\n",
    "    xt.append(float(x[0]))\n",
    "    yt.append(float(x[1]))\n",
    "    zt.append(float(x[2]))\n",
    "    dxt.append(float(x[3]))\n",
    "    dyt.append(float(x[4]))\n",
    "    dzt.append(float(x[5]))\n",
    "    ddxt.append(float(x[6]))\n",
    "    ddyt.append(float(x[7]))\n",
    "    ddzt.append(float(x[8]))\n",
    "    \n",
    "    Zx.append(float(Z[0]))\n",
    "    Zy.append(float(Z[1]))\n",
    "    Zz.append(float(Z[2]))\n",
    "    Px.append(float(P[0,0]))\n",
    "    Py.append(float(P[1,1]))\n",
    "    Pz.append(float(P[2,2]))\n",
    "    Pdx.append(float(P[3,3]))\n",
    "    Pdy.append(float(P[4,4]))\n",
    "    Pdz.append(float(P[5,5]))\n",
    "    Pddx.append(float(P[6,6]))\n",
    "    Pddy.append(float(P[7,7]))\n",
    "    Pddz.append(float(P[8,8]))\n",
    "    Kx.append(float(K[0,0]))\n",
    "    Ky.append(float(K[1,0]))\n",
    "    Kz.append(float(K[2,0]))\n",
    "    Kdx.append(float(K[3,0]))\n",
    "    Kdy.append(float(K[4,0]))\n",
    "    Kdz.append(float(K[5,0]))\n",
    "    Kddx.append(float(K[6,0]))\n",
    "    Kddy.append(float(K[7,0]))\n",
    "    Kddz.append(float(K[8,0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimated State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x106e05a10>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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aa9uGPS/mLauXgo4OePBB18X5Rz+CiopY10hEREREZOpcTMuqmXSb39SIRhz6l3/5Fz7x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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10842d3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.subplot(211)\n",
    "plt.title('Estimated State (elements from vector $x$)')\n",
    "plt.plot(range(len(measurements[0])),dxt, label='$\\dot x$')\n",
    "plt.plot(range(len(measurements[0])),dyt, label='$\\dot y$')\n",
    "plt.plot(range(len(measurements[0])),dzt, label='$\\dot z$')\n",
    "plt.legend(loc='best',prop={'size':22})\n",
    "\n",
    "plt.subplot(212)\n",
    "plt.plot(range(len(measurements[0])),ddxt, label='$\\ddot x$')\n",
    "plt.plot(range(len(measurements[0])),ddyt, label='$\\ddot y$')\n",
    "plt.plot(range(len(measurements[0])),ddzt, label='$\\ddot z$')\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x109488b90>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JkrRPo5mkvgD4WEppSXX7QwAppT0+LjcipgG/TSkt6Ffe0ElqrWKhyA//+xs8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\nEREREZGo8f8Bmk5hoHobrVQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b72750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.subplot(311)\n",
    "plt.plot(range(len(measurements[0])),Px, label='$x$')\n",
    "plt.plot(range(len(measurements[0])),Py, label='$y$')\n",
    "plt.plot(range(len(measurements[0])),Pz, label='$z$')\n",
    "plt.title('Uncertainty (Elements from Matrix $P$)')\n",
    "plt.legend(loc='best',prop={'size':22})\n",
    "plt.subplot(312)\n",
    "plt.plot(range(len(measurements[0])),Pdx, label='$\\dot x$')\n",
    "plt.plot(range(len(measurements[0])),Pdy, label='$\\dot y$')\n",
    "plt.plot(range(len(measurements[0])),Pdz, label='$\\dot z$')\n",
    "plt.legend(loc='best',prop={'size':22})\n",
    "\n",
    "plt.subplot(313)\n",
    "plt.plot(range(len(measurements[0])),Pddx, label='$\\ddot x$')\n",
    "plt.plot(range(len(measurements[0])),Pddy, label='$\\ddot y$')\n",
    "plt.plot(range(len(measurements[0])),Pddz, label='$\\ddot z$')\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kalman Gains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x109c4ca50>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A+L/QemD/Ce3D3W4Ar0Cb6woAC6H1CJVBm1/6Zr066v/d3LmYewU/z+sEtA9SAHBRRD5t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\nloyYPr9rFy2KFKFn2bK58t5Zbd4MgwbB1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+Bijo/fH9932+PD+9r+fJJ1c25+hMvOz90C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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107344c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.plot(range(len(measurements[0])),Kx, label='Kalman Gain for $x$')\n",
    "plt.plot(range(len(measurements[0])),Ky, label='Kalman Gain for $y$')\n",
    "plt.plot(range(len(measurements[0])),Kz, label='Kalman Gain for $z$')\n",
    "plt.plot(range(len(measurements[0])),Kdx, label='Kalman Gain for $\\dot x$')\n",
    "plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n",
    "plt.plot(range(len(measurements[0])),Kdz, label='Kalman Gain for $\\dot z$')\n",
    "plt.plot(range(len(measurements[0])),Kddx, label='Kalman Gain for $\\ddot x$')\n",
    "plt.plot(range(len(measurements[0])),Kddy, label='Kalman Gain for $\\ddot y$')\n",
    "plt.plot(range(len(measurements[0])),Kddz, label='Kalman Gain for $\\ddot z$')\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "plt.legend(loc='best',prop={'size':18})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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d2X33l8el3XTTTQ29vggJqtFBEgIuAoYBR3UnJ0kDJb29CfGZmVmHanSY+deB\nHYBjI2IDJMkJOAvYLePYzMysSdpqFJ+ko4F9gTOB70gali46EFgaEV9pQnxmZtYERWjiqytBSdoC\nOBo4PCI2SVoEXA28HvgpcFLzQjQzs6y1TYJKm/OOKZleAry1WUGZmZn5flBmZh2obWpQZmbWXoqQ\noHzLdzMzyyXXoMzMOlARalBOUGZmHagICcpNfGZmHSjrE3UljZU0T9KDkh6Q9Pka236rpA2S/qVW\njK5BmZlZFl4CvhgR90oaCvyPpBsi4uHSldKrD80E5gI1q3GuQZmZdaCsa1ARsSIi7k2fPw88DOxY\nYdOfA35GcuPbmlyDMjPrQM3sg5K0K8ml8W4vm78T8AFgIsnFHqJWOU5QZmYdqNEE9eCDD/LQQw/V\nU+5QkhrSF9KaVKlvA1+OiEjvjlEzCCcoMzPr0d57783ee++9efrnP//5q9aRNAj4OXBFRPyyQjH7\nA1emyXEU8B5JL0XENZW26QRlZtaBsm7iS2tE3wceiohvV1onInYvWf9SYE615ASgiJpNgJmQFM88\n80zTt9OokSNHtjqEqvrjuPTGjBkzWh1CVdOmTWt1CBXl9VgCbLnllq0OoaLVq1e3OoTC2XbbbYmI\nurKOpLjqqqv6tL1jjjnmFduT9E7gd8D9vNy3dDKwC0BEzC6LoTtBXV1tG65BmZl1oKxrUBGxkAZG\nhkfE8T2t42HmZmaWS65BmZl1oCJc6sgJysysAzlBmZlZLhUhQbkPyszMcsk1KDOzDlSEGpQTlJlZ\nB3KCMjOzXCpCgnIflJmZ5VJdCUrSKZKekzQxnT4snT65ueGZmVkzZH0/qGaot4lvJ2Ao0H3xulHA\nsHS+mZkVTBGa+OpNUJ8BTo+IFQARcaWk+cBTzQrMzMw6W10JKpLLMa8om7eiyupmZpZz7VSDQtJI\n4DSSOyDuAVwM3AicC7wIbAdMi4gnmxCnmZllqG0SlKTBJDeiOjEilkp6M3AnMAeYAhxFkrDuBc5r\nUqxmZpaRIiSoeoeZTwHOj4il6fR6YBBwT0SsIrk51X0kCcvMzKzP6m3iezYi5pVM75f+nQsQEZcA\nl2QZmJmZNU8RalD1DpK4omzWocBzwN2ZR2RmZk3XNgmqgonAwnR0X11mzpy5+fnBBx/MO9/5zl5u\n2szMbr75ZhYuXNjr17dlgpK0MzAOuKhs/vERcWm1102bNq3x6MzMrKLx48czfvz4zdMzZsxoYTTN\n0eMgCUkq0jz6AAAPIUlEQVSjJd0h6ax01qT0710l6+wJ7NWE+MzMrAmKcKmjekbxTQAOAP4uaQjw\nXmAlMBw2nx91FvC1ZgVpZmbZKkKCqqeJ7zqSc6DGALOALwJjgVMlHUWS5KZGxJqmRWlmZplqiz6o\niFgHfLps9uPA4c0IyMzMDHzDQjOzjtQWNSgzM2s/TlBmZpZLRUhQvuW7mZnlkmtQZmYdqAg1KCco\nM7MOVIQE5SY+M7MOlPWJupIukfSUpD/U2GaXpHskPSBpfk8xOkGZmVkWLuXlS+G9iqTtgO8CR0bE\nG4HJPRXoJj4zsw6UdRNfRNwsadcaq3wY+Hn3jW8j4pmeynQNysysA7XgWnx7ANtLmifpLkkf7ekF\nrkGZmVl/GERyN/Z3AdsAt0n6fUQ8Uu0FTlBmZh2o0VrQ3XffzT333NOXTS4BnomI9cB6Sb8D9gGc\noMzM7GWNJqj999+f/ffff/P0JZdc0ugmfwXMkjQQGAwcBJxX6wX9lqBGjhzZX5uq26pVq1odQlV5\n3F8AU6dObXUIVc2cObPVIVSU57tJ5/UzMGLEiFaHUNXq1atbHUImsh4kIenHJPcPHCVpCXAaSbMe\nETE7Iv4oaS5wP7AJuDgiHqpVpmtQZmbWZxFxXB3rfAP4Rr1lOkGZmXWgIlxJwgnKzKwDOUGZmVku\nFSFB+URdMzPLJdegzMw6UBFqUE5QZmYdyAnKzMxyqQgJyn1QZmaWS3UnKEmnSHpO0sR0+rB0+uTm\nhWdmZs3QgquZN6yRJr6dgKFA9zV4RgHD0vlmZlYgRWjiayRBfQY4PSJWAETElekte59qRmBmZtY8\nbZWgIiKAFWXzVlRZ3czMrE/qTlCSRgDfJLlM+iDguIjYWLJ8FjAiIj6SeZRmZpaptqpBAWcCpwKr\ngbXAZcC1AJIGAccD12UdoJmZZa9tEpSkPYGVEbFU0pHp7JUlqxwAbA3clHF8ZmbWBEVIUPUOMx8N\nXJo+PwFYHBF3lCw/JP07L6vAzMyss9VVg4qIWwAkjQGOAKaXrTIeeCoiHs40OjMza4oi1KAavdTR\nZGAgcFX3DEkDgIOBubVeOH369M3Pu7q66OrqanDTZmbW7eabb2bhwoW9fn07JqiDgOUR8UjJvDcB\n29JD815pgjIzs74ZP34848eP3zw9Y8aMFkbTHI0mqNcAfymbd1j61/1PZmYFUYQaVKMXi70T2DVt\n1kPSviRDz5eV1arMzCzH2u1afABfA3YBrpW0CHiepE/qt1kHZmZmzVOEGlTD94OKiI93P5c0GdgG\nuDzLoMzMzBq53cb1wNOShqXTA4AvAb+MCJ+ga2ZWIO3WxHcAcCvwvKSBwPnAi8BHmxGYmZk1T7s1\n8R0LvBu4ABhDkqw+HxGbmhGYmZk1T1slqIi4EbixibGYmZlt1vAgCTMzK762qkGZmVn7cIIyM7Nc\nKkKCavRKEmZmZv3CCcrMrAM14zwoSZMk/VHSI5KmVVi+raQ5ku6V9ICkT9SK0U18ZmYdKOsmvvT8\n2FkkFxBfBtwp6Zqy+wR+FnggIo6UNAr4k6QrImJDpTKdoMzMOlAT+qAOBB6NiMfT8q8EPgCUJqhN\nwPD0+XBgVbXkBG7iMzOzbOwELCmZXprOKzUL+EdJy4H7gC/UKtA1KDOzDtRoDeq2227jtttuq7VK\n1FHMJODuiDhU0uuBGyTtExFrK8YYUU+ZfSMp+mM77WTVqlWtDqGiESNGtDqEqvL6P3buuee2OoSq\nPvvZz7Y6hIo2bcrvFdS23377VodQUUQQEXVlHUmxZMmSnlesYezYsa/YnqS3AdMjYlI6/RVgU0TM\nLFnnv4FzIuKWdPq3wLSIuKvSNtzEZ2bWgZowiu8uYA9Ju0rakuT6rdeUrfME6V3YJY0B9gIWV4vR\nTXxmZtZnEbFB0onA9SQ3sv1+RDwsaUq6fDZwJvADSfcDAqZGxLPVynSCMjPrQM24kkREXAdcVzZv\ndsnzJ4F/qrc8Jygzsw7kSx2ZmZn1kmtQZmYdqAg1KCcoM7MO5ARlZma5VIQE5T4oMzPLJdegzMw6\nUFvVoCSdIuk5SRPT6cPS6ZObF56ZmTVDM+4HlbVGalA7AUOBken0KGAYr75arZmZ5VwRalCNJKjP\nAKdHxAqAiLhS0nzgqWYEZmZmna3uBJVejnxF2bwVVVY3M7McK0INquFRfJLGSbpV0hpJF0saKmmQ\npJ9I2r0ZQZqZWbaK0AfVUIKStBUwB1gJXEnSD/VjYBFwe0RUvWy6mZnlRxESVKPDzLcHJkfEg90z\nJJ0DEBHnZRmYmZl1toYSVEQsB5Z3T0uaAbyd5Da+ZmZWEEXog+rVibpK3tks4A3ApIhYn2lUZmbW\nVG2ZoCQNAC4lOR/qiIh4sZ7XTZ8+ffPzrq4uurq6Gt20mZmlkoHVvdd2CSqtOV1EcoLuURGxIZ0/\nEDgwIm6r9trSBGVmZn1TnmD6mrDyqNFh5l8HdgCOLUtOZwG7ZRybmZk1SVuN4pN0NLAvcCbwHUnD\n0kUHAksj4itNiM/MzJqgbZr4JG0BHA0cHhGbJC0CrgZeD/wUOKl5IZqZWdbaJkGlzXnHlEwvAd7a\nrKDMzMx8Pygzsw7UNjUoMzNrL0VIUL7lu5mZ5ZJrUGZmHagINSgnKDOzDuQEZWZmuVSEBOU+KDMz\nyyXXoMzMOlARalBOUGZmHagICapwTXzz589vdQgV5TUugIULF7Y6hIryvM/yGtvixYtbHUJVN998\nc6tDqCiv///Q2iuQN+NisZImSfqjpEckTauyzgXp8vsk7VsrRieojOQ1LoBbbrml1SFUtGDBglaH\nUFVeY8tzgsprIshrXO0mvbPFLJI7rP8jcJykfyhb5whgXETsAfwbcGGtMguXoMzMrO+aUIM6EHg0\nIh6PiJeAK4EPlK3zfuAygIi4HdhO0phqMboPKqeybB/uz/u32KsNHTo0s7K23HLLTMvL+v8iq/Ly\nGhfAjjvumFlZa9asYfjw4ZmUtWzZsobWb8J3wk7AkpLppcBBdayzM/BUpQLVH22gktrvVo9mZjkT\nEXVlnay+k0u3J+mDwKSI+HQ6/a/AQRHxuZJ15gAzIuKWdPpGYGpE3F2p/H6pQdW708zMrPma9J28\nDBhbMj2WpIZUa52d03kVuQ/KzMyycBewh6RdJW0JHAtcU7bONcDHACS9DfhrRFRs3gP3QZmZWQYi\nYoOkE4HrgYHA9yPiYUlT0uWzI+LXko6Q9CiwDji+Vpn90gdlZmbWKDfxmZlZLjlBWb+TtKWkO9Iz\nzrdvdTxFkLd9JukUSc9JmphOH5ZOn9zq2PLM+60xTlDWCluQnA/xWmCbFsfyCnlLBCXyts92AoYC\nI9PpUcCwdH5L5TwJ5Ha/5ZH7oKwlJG0NDIqINa2OpZSkbYBHSL5E9o6I8mGyLZOnfabkLM8xEbGi\nZN4OwFPR4i8VSReSXEbnQxHxU0kfAn4EXBgRn21xbLndb3nkBNVLkkYA3wQGA4OA4yJiY8nyWcCI\niPhIi0K0XspTIrDGOQm0Dzfx9d6ZwKkkv9Qmk1wgEQBJg0iGTw5uTWj5JWlkejXj70iaK+mDkraV\nNDudf7mk17YyxohYn7fkJGmcpFslrZF0saShkgZJ+omk3VsUUy6PZSRWlM1bkafklMfjmUe5Pw9K\n0kjgNEDAHsDFwI3AucCLwHbAtIh4sh9j2hNYGRFLJR2Zzl5ZssoBwNbATf0VUyWSxgGXA28EfgJ8\nkWSfXQF8JSL69dLYkgYD3wdOTPfdm4E7gTnAFOAokuN7L3BeP8eW2xqxpK1I9tGfSS7AORr4MbAP\n8O3+Po5pTD6WvY8vd8cztyIitw+Sf7BfAjun028m+YL9GUkn46eATcBJ/RzXwcAu6fNfkVzBt3T5\ntDSuf2jhvtsKeDiN7yLgFyQfiif6e3+VxPR54NCS6T3S/fTVdPqTwD3AHi2IbRbJZVeGpDG9t2TZ\nIJKTCn/Wov22I0l/WOm8c4A5Lfz/8rFso+OZ10fea1BTgPPj5Y7q9ST/YPdExKr0gof3kXzx9pt4\n+UKHY4AjgOllq4wnae9+uD/jKrM9MDkiHuyeIekcgIjo11+0JZ6NiHkl0/ulf+cCRMQlwCX9HVTe\na8QRsRxY3j0taQbwdkqalVvAx7KXcno8cynvCSqXH4ISk0ku6XFV9wxJA0hqWHNbFRTk80MQEVeU\nzToUeA6oeCXjfjQauDR9fgKwOCLuKFl+SPp3Hi2Udv7PAt5ActXo9a2Kxcey7/J0PPMq1wkqxx+C\nbgcByyPikZJ5bwK2JQcfAMj9h2AisDDSNo5WKUKNOP3hcylJ0/YREfFiq2KpwseyAQU4nrlQtFF8\nufgQlHgN8JeyeYelf1ueoNIPwQ+A15F8CHKTnCTtDIwDFpTNr3nxyCarVSOe36KYun9kXERyQudR\n3V9mkgZKenur4urmY9mYvB/PPClMgsrph+BOYNf0Hx9J+5IMPV9WVqvqd3n7EEganV6h4ax0VndT\n410l6+wJ7NXfsZXIa43468AOwLERsQGS4wicBezW38H4WPZZro5nnuW2iU/SaOBa4DcRcQr5/BB8\nDdgFuFbSIuB5kl9tv21hTN26PwT/XOFD8Afgtn6OZwJJB/V/SxoCvJek83p4GtvINLYT+jmuUrmr\nEUs6GtiX5Ly770gali46EFgaEV9pQVg+lr2U0+OZX60eRljtQVJF30RSIxlCMkz6KeD96fKRJNX3\n4S2McesqMU9s8b47miRJdgH/CfwwfTwCzGtRTENIzov5Lknb+64k/QE3kAx0+QGwa4v325kkd/cc\nkE7vS9LnuaRF8WyR/o93xzOWpNb+LDAbGOJjWYxjmefjmedHbi91lP4y+zbwd5KLY55OckBPBZaQ\nNE9Oj4jHWxTf9cA7gB0jYm3azHcbSfPev7QipjSuLUiuO/ahiNgkaSxwNfB64Kck50Cta1V8eZZe\n4ug/SX59d9eITyQ5Z+YTLQzNGuRj2R5ym6DyTtIqkubGSSTJ8nySE4nf4wRQTJK2jpKBJJImk/zi\nPSwiWnpVEGuMj2V7cILqJUmHAe8mOelvDHArcEFEbGppYNYrea0RW+N8LNuHE5QZrhG3Ex/L9uEE\nZYZrxO3Ex7J9OEGZmVkuFeZEXTMz6yxOUGZmlktOUGZmlktOUGZmlktOUGZmlktOUGZmlktOUGZm\nlktOUGZmlkv/H2DcZ0JtPJM3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10857ea90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Covariance Matrix $P$ (after %i Filtersteps)' % m)\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(10))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,8.5])\n",
    "plt.ylim([8.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Position in x/z Plane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Za88uy22j7HiPFHzFFe55+d16P/+85G69pWGMOeVvQM8/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\nMifx67SjfQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b50990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "plt.plot(xt,zt, label='Kalman Filter Estimate')\n",
    "plt.scatter(Xm,Zm, label='Measurement', c='gray', s=30)\n",
    "plt.plot(Xr, Zr, label='Real')\n",
    "plt.title('Estimate of Ball Trajectory (Elements from State Vector $x$)')\n",
    "plt.legend(loc='best',prop={'size':22})\n",
    "plt.axhline(0, color='k')\n",
    "plt.axis('equal')\n",
    "plt.xlabel('X ($m$)')\n",
    "plt.ylabel('Y ($m$)')\n",
    "plt.ylim(0, 2);\n",
    "plt.savefig('Kalman-Filter-CA-Ball-StateEstimated.png', dpi=150, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Position in 3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UhvBlL5Sai8gCNxRJPEHS5/NFHNrKIElERB3BsEhEFAGXvUgdBub4tSdIiq9n\ni8XCIElERDExLBIRBWnvshdqxG1Ob9Fetz6fT/o6eySJiCgWhkUiSnvRlr1Idi8ih6FSMkULfuJr\nkEGSiIgYFokobaXDsheR1vojiiXWWpLxBMnwMBlcuZWIiLSFYZGI0o64REFwL6IaQiKXziC1iydI\nBr+3gjFIEhFpD8MiEaWFaMtesJFK6UYQBEWGWMsZJMUQySBJRJRaDItEpGtiL6LSy14QUXRyBEmj\n0Qiz2cwgSUSURAyLRKQ70XoR1b7shcFgkLaXKF0kEiQ9Hk+r3xWHtEYquENERB3DsEhEuhG8LqLW\nl70gosSCZHgxJ/EGUbTKrURE1DaGRSLStOCFx8XFxrXQixgJl84gil88QVIchs4gSUTUPgyLRKRJ\nwesishdRPxiYSQ7tDZJi8Z/gYa3BYZLXFyJKNwyLRKQZYi+i2+1GIBAIWQicjTgiiodSQTLaYxIR\naRnDIhGpntiL6Pf7EQgE0NTUBLPZDLvdnupNkxV71YhSS66hrcF/84YWEWkZwyIRqZbYKBPL6bPR\nRUSp0p4g6fF4YLFYovZI8ppGRGrHsEhEqhJt2YvwO/h67YGTe7/YCKVw4T1i1HHRgqTf75dGQIhB\nMpLgEGkymaReSgZJIko1hkUiUoXwZS/auuOux7DIRiGRPrV1LRODpNfrbRXmGSSJKJUYFokoZYIb\nSYkse6HnnkW5sReJSN06EiRjLf/B9z0RyYFhkYiSrqPLXhgMBmmIqp4wBBPphxzv5baCpDgig0GS\niJTCsEhESRHcsEmkF5E6jr2LRKmj1HsvkSAZjkGSiOLFsEhEigpf9gJIrBcxEr32wMm9X+Jx1tKx\n0tr2EqkRgyQRyYVhkYgUoeSyFwwURKR2au3Rj6dwGIMkEYkYFolINvEse0FEROoUz1qSsYJkpDDJ\nzwAibWNYJKIOC65oGs+yFx2l155Fve4XEWlfPEEyeDRJsEhBMngJECJSL4ZFImqXaL2ILFhDpG5q\nHR6pN+l0nBkkifSLYZGIEhJc0bQ9y17IQa89cHrdLyJKX3IGSTFEMkgSJQ/DIhG1SY3LXjBUERFp\nW0eCpMFgkHoiIxXcISJ5MCwSUVTishc+ny9lvYiRpPr5lSbn8DX2VhKlRjoNQ1VCIkFSPNY+nw8G\ngwFmszlm5VYiih/DIhGFEHsRw5e9UNNcRL0GIDZiiIjaFi1IBn9miYXXwkO7+HnGIEkUH4ZFIgLw\nXS+i3+9ffoLGAAAgAElEQVTnshdERKQ5giDEXK5DvMnIIEkUP4ZFojQnfmgG35FVe0jUa88i8N2+\nqfn4K0nP55bSSzq/j1OlrWMez9DWSEFSDKHB8yODw2S0xyTSA4ZFojQUbdkLrX3YsTFGRERyUCJI\nauHmK1FbGBaJ0kj4shda/SDT2vamiji0OBAISGXniYj0SqkbiO0NkuLvMEiSljEsEulctF5ENRWs\naQ+9DteUYximIAhwu91wu90hDRkAIXNwuPh1etLj+0aNeJzTQ6wgCXz3GRxvkAy+JvP1Q2rAsEik\nU+G9iIA2h5pS/Px+P1wuFzweD8xmMxwOBwwGg7Q2pljpNhAIIBAIwOv1Sv8PbqCEh0m+ZohIC9QY\n0GNdQ4ODZCTBIZJBklKFYZFIR8Qw4PF44HK5YLPZdNGLGIleC6Ekul+CIMDr9cLtdsPn88FmsyEn\nJwcmkwkAWhUuAiB9L/gxgkOk+Jjiv4MDZPi/2WAhImqfeIOkeGMv+GcZJClZGBaJdCB4XUTx3263\nGxkZGaneNMXoNSzGKxAISDcFDAYD7HY7srKy2tVIEBsXkW4qhAdJsfEiBslYvZFssFA6U2Mvl97p\n6Zh3JEjGWv5DL8eHkodhkUijxEZ8pGUvTCZTWgcpPQseamqxWJCZmQmz2RyzAdCRBlRbQVIMjcEN\nl/D5kZHCJBGRnNLpM6+tIClOQ/F6va2+zyBJiWJYJNKYeJa9SIcPTb32LEbaL3FYqMvlgt/vh81m\nQ25ubsqHF4s3JiKJ1BsZKUiGB0oioo5I98DDIElyY1gk0gixwR3Pshdi4NDTkJx0FAgEpKqm4lBT\nq9WqiXMqBslo8yNjFdoRBAEul4uNFdI0cZg2JQc/79rGIEntwbBIpGLtXfYiHS7ceu5Z9Pl88Hg8\n0lDTrKwsmM36uFy3VWgnEAigubkZRqORhXaIiJKkrSAJoFWQDA7oRqMRVquVQVKH9NH6INKZ8GUv\n2lMwRK/rEAbTU1gUg5HP54PP54PdbpdlqKmWzn/wjRCr1RryPRbaIaJY9P55l0qx1pIUK7CL1+dw\n4vU4vFeS12btYFgkUongISDimksdmcel1543kV4+ZIKHmoofona7HTabLdWbpiostCMfNqqTg8eZ\n0kFwz2Kk0SIAQgrxBYsUJIOXACF1YFgkSrHwZS+A2MNBEn1svdJ6GPb5fHC5XPB6vSFDTRsaGlK9\naZqjRKEdNlSItIXhPHWiHfu2eiSB+IIkAHz99dcoLy+Xc7MpTgyLRCkQbdkLOYsh8ENTfcThOm63\nG4FAADabDQ6Hg0UwFNSRQjuxhrYSEdF3Er0uJhIkz549i7vuugtvvPFGxzeUEsawSJREYkAU51oB\n8vUihtN6z1tbtLR/4lBTl8sFk8kEu90Oi8USs5ItKautQjvBIZKFdqg92NOVXDzeqSP3sQ8PkrW1\ntcjLy5Pt8SkxDItESSAOfwvuRVS6YZkOoUPN+yfeGBCHmlqtVmRnZ+umqqmetTU/koV2iNSHYTF1\nlD72VVVVyM/PV+zxKTa2WogUEm3Zi2R9mOk9LKp1/8Shpi6XC4IgpHyoKRtP8mKhHSKiUEqHRafT\niYKCAsUen2JjWCSSmRzLXsi5LXplMBgilulOlUAgAJfLBbfbDZPJhIyMjKhDTWNRawhONi32ErDQ\nDgXT4mtYy3i8U0fpz6yamhr2LKYQwyKRDKL1IqaycAk/NJUn3hhwuVzw+XywWq3IycmJGhiobXp9\n3bLQDhHpUXAVd6VUV1ejrKxMscen2BgWiTogvBcRSO5Q01j03kOVyv0TBEFaG1EQBNjtdmRlZcly\n3vV+3igUC+0QyUOcM0ypwWGo+sWwSJQgsQEnhkQg9b2Ikeg9dKRi//x+vxQSzWZzu4eaEsVDiUI7\nwY9NyuKwSEoHyXidO51ODkNNIYZFojgFr4uotl7ESNQ2p0+rONSU1KgjhXYAwOVysdAO6QrDeWok\nKyyyZzF1GBaJYhDv3id72Qs5sGexY4KHmgKAzWaTbahpLEqEfLW/VklesQrtBAIBNDU1wWQysdAO\n6YqeP+/ULBnHnWExtRgWiSIQA6I4rAtQdy8iyUdcG9Hj8cBsNsPhcMBsNvPcky6Ir2OLxRLydRba\nkReDS2rwtZgaSh93t9sNu92u6HNQdAyLREHEO+1qWPaio9izGD+xcIjb7YbP54PNZkvZUFO9nzdS\nJxbaUUa6738ycRhqaih93JNRbZViY1iktKfGZS/kkA6ho6P7Jw41FedvyVnVlEgvlCi0wyBJpA/J\nCum8XqQOwyKlrfBlL/TWgNF7WOzIeQoeamqxWJCZmanboaZ63CdSj44U2onUG6mX+ZHs5Uo+HvPU\nUPq4e71eFpRLMYZFSitaWfZCDukQFhPZP3HonMvlgt/vh81mQ25ururOvd7PWzzEY8CGn7bFKrQT\nqTeShXaovdL9mplKSl+ra2pquGxGijEsUloIrmja1NQEo9EIu93OhkcaCAQCUlVTcaip1WrluSdK\nITFIRpsfyUI71B58DaSGksfd6XQiLy9PscentjEskm7FWvZC/Lee6b2Hqq398/l8cLvd0lDTrKws\nmM3auOTp+bxRaqm9x1YvhXbUfpyJ5KL0a72qqoo9iymmjZYTUQLaWvZC7yFKlC77GfxBFT7U1G63\nq3KoaSxsYBJFxkI7FA3Deeoofey5xmLqMSySboiNg/BexPCLmBKLnquZXj9Eg/cpeKip0WiEzWbj\nUFOiNMJCO+lNr59zWsA5i/rHsEiaFm3Zi1gXrnTpcROPg94/RBsbG+H1ejU31DSadHl9EiVLKgrt\n6P26SyRS+vOquroaZWVlij4HxabtVhWlLfFDvT3LXrAxrm2CIMDj8cDtdgNoacxpbagpEakDC+3o\nA8N5aohtKQ5D1TeGRdKMaL2IiYaEdAqLetpXcaipy+WCyWSC3W5HY2MjbDabroKins4ZkVZ1tNCO\n+D72eDwMkqR7SodFDkNNLYZFUr3gdRGD72K19+KUTo1xre+rWKzI5XLB6/XCarUiOztbGmra3Nys\n6f0jIu2Jp9COx+NhoZ0kYs9iaiTjuLNnMfUYFkmVxA9cMSQC7etFjETrASoRWt1XsbHlcrkgCAJs\nNhscDoeuehApOq2+bonE0Cf2Rtrtdul7LLRDesOwmB4YFklVgtdFlKMXMZJ0aohqbV8DgQBcLhfc\nbjdMJhMyMjJgsViinn+t7V889LhPRJSaQjvpgj2LqZGMzyq32x1y04WSj2GRUk7sRYxn2Qs5iI3x\ndPlwUXvwEHuQ3W63NNQ0JycnaqOKiNovXa57qZbocWahnY5R++ecnin5OktGAR1qG8MipYwYEMX5\nHID8vYiRpNNFR837Gj7U1G63IzMzM+EGlt4aCUrsk5pfB0QUXUcL7UQa2qrXIKnHfVK7ZN184rlN\nLYZFSrqOLHshl3RYfxBQZ5jy+/1wu91wu90wm81tDjVti9r2j4goGeIptBM+tFWvhXbEfaLkUrod\n5fV6OcpIBRgWKSnkWvZCLmoMUUpQy36KQ01dLhd8Pp9sQ0212KiJVzrczCDSq1S/f9sKkiy0Q3JQ\n+nVeU1PDZTNUgGGRFBW+7IVa7lyqJUQpLdX7KQiC1IsIADabDVlZWbKd/1TvnxKUeG+kuuFKROqh\nx0I7vMbpU3V1NfLy8lK9GWmPYZFkF3y3Uu5lL+Six5ARTSr2U1wb0ePxwGw2w+FwwGw288OciEjF\nWGiHEqH08N/q6moum6ECDIskm2QseyGXdAmLyTz2YnEFt9sNn88Hm82meFVTvZ5HuefUpsscXSK1\n0NscOrUX2uH1LTWUPu5Op5PDUFWAYZE6RPyQEIeaAurrRYxEryEjXDL2Uxxq6nK5YDAYYLfbZR1q\nGs/zU3RabUDxvBJpAwvtpC/OWUwPDIvULqla9kIuDIsdFzzU1GKxIDMzM+lDTdPlPKYbrVxHiCi2\nZBXaYc9iaih93Kurq1FWVqbY41N8GBYpIeIF3efzAYBm7wCmS8iQez/F4UUulwt+vx82mw25ubkp\nrWorNiz0JF1en5R8bFQnB49z2+QstMPrpT45nU7OWVQBhkVqU7RlL7T8QZgujXG59jMQCEhVTcWh\nplarVdOvASIiUqdEC+0AQFNTEwvtJJF4HjhnUf8YFimq4Iqmalr2Qg567ZGSm8/ng9vtloaaZmVl\nwWxWz2VDr6Ffr/tFRNQRkQrtCIKAxsZGOBwOAEhpoZ10pPQwVPYspp56Wn2kCtF6EdVesCZR6dIY\nb89+hg81tdvtKR1qGku6nEci0hYOQ00+8TOKhXaSIxmv8ZqaGoZFFWBYJAAIqWiq9mUv5JAuISOR\n/Qweamo0GmGz2TjUVEfYeCUiPYrn2pasQjvpJBmfKW63G3a7XdHnoLYxLKax4GUvGhoaYLfbpYug\n3qXLMNR4wqLP54PL5YLX61XlUNNY9Br65dov8dx6PB4AbPQQEYWTs9BO8JxJ6pjgjgtKLW20CElW\n4rIXPp9PejN6PB5kZGSkzZsyXfZTFH4HUBAEeDweuN1uBAIB2Gw2OByOtLhRoHfBw4jFc5uVlRVy\n5zy80RN8151FIYg6jj35yaPksU600I74/3QotJOs17hejpeWMSymCfGiFr7shRgO9NpDE0069SwG\nE4eaulwumEwm2O12WCwWzV6M9fq6be9cU/Hchles9Xq90vs9WqMnnqIQ7I0kIrVJxWdApEI7wduT\nyDU1OFhq6bqqdFj0er1Re3wpuRgWdU4MiOJEbiDyXEQxPKXLGzPd1mXyer3weDzwer2wWq3Izs7W\nzFDTWPQaFhPh9/uluaZmsxmZmZkwm81xf4jLMZdH7jvnPK9ElAg1hay2rqnhIzyCr7NaKrSjdFis\nqanhshkqof3WIkUkXoSCexFjXWzSLTyJ9DxUSBxqCgCNjY2w2+0caqojXq8XbrcbXq8XNpsNOTk5\nst/siTaXJ9oQrFi9kWpt8KQbPV/z1ITHOXm0dKz1VGhH6eNeXV2NvLw8xR6f4sewqCPRlr2I582c\nbnfyxeOipQ+ZeAUCAbhcLrjdbphMJhiNRmRmZsJisaR602Sn19dttP0SbwC4XC4IggC73Y7MzMyk\nv4YTGYLFghBERG1rb6GdSHPO9XBd5RqL6sGwqAPhy1605w6+Xhvdsehpn8XXgNjTZLVapZ6murq6\nVG8edVD4siYZGRkJzTVNZoMhnjvnbfVGig2g4IYQEVEkerzpG06NhXbEYbNKcTqdHIaqEgyLGhWt\nF7G9b9x0KfgSTA9hMd6eJq3vZzR6OIeRiPvl9/ulpS+0tqxJJG01eIILQvh8Pqlis9qGXxHFosdr\nEqlTKgvtcM5i+tBuqyNNhfciAvEPNY3FaDTC7/fLsYmaoeWgEV7UJFZPUzo0qPV0Zzn4RlBzczNs\nNhtyc3N1Pdc0vDdSLLZlsVjaHH6l9/L0pF18DSaHnq7/clK60E4y5iyWlZUp9vgUP4ZFjRDvCImB\nriO9iJFoOTi1l9b2WbxR4HK54PP5QoaaxqK1/UyEnhoIwb3EgUAAZrMZOTk5su2jVhtUifRGBt81\nj9TYYW8kEZE8hXbE74lfk/va6nQ6OWdRJRgWNULp+Tt6DhTRaGWfxfXz3G43AEiLrCcyX00L+9le\nWi9UFL72ZUZGBrxeL4NNG+KdGykO541VDIK9kSQnLV+PtEjpuXPpJt5CO+IoN3E6lNyFdjhnUT0Y\nFjVEyeUtOGdRfYLnq5nNZjgcjoTWzxOpfT/TlViQyOPxtFr7Ulzyhtonnt5I8W8u+UGkbQznySNe\nW41GI9xuN+x2u9TGkLvQjtqqoR47dgwLFy7Et99+C4PBgBtuuAG33nprqjcrKRgWNUTJRn86rrOo\nxhAlDqVzu93w+XyyrZ+ntv2UkxrPYzTi+XW5XPD7/bDb7RHnI2ppn5Sg1P7LMfRKT6XpiYg6Qrz+\nyVFoZ8eOHTh8+DD69OmDPn36oKamRlVh0WKx4NFHH8WwYcPQ0NCAkSNHYurUqRgwYECqN01xDIsE\nID0bp2raZ3GoqcvlgsFggN1uT2ioaSxq2k8laGH/Ip1fq9WatKDBQNO2aEOvxNdWPEt+tKeiYLKx\nF0Z5PMbJxeOdfIkc83gL7fj9fhw4cAB///vf8e9//xvnzp3DhRdeiL59+6KsrAx9+/aV/nTp0iXp\n57xr167o2rUrACArKwsDBgzAyZMn0yIsGtpoZKm7BZZmgu9yy00QBDidTuTl5aXNRVfs3cnMzEzZ\nNoQvjWCz2do11DQWNeynkmpra5GZmanKJSUCgQBcLpdUtdZut8d1fpubmyEIAhwOhyzbIfaSaWVe\nj9vthsFggNVqTfWmxBR+xzz4zrlal/zweDwQBAE2my1l26B3YrVqud6/FFtTUxNsNluHR+BQ/JR+\njQuCgEsvvRRPPvkkDh8+jC+++CLkb7fbjbVr12LSpEmKPH9bjhw5goqKChw8eBBZWVkp2QYFRP1g\nUl/riqJSsoGRrFLIapKqHqnwoYhKL42ghZ63jlDj/olVa71eb9xVa4Ol4xxiLYq3yI5YDCIZC2UT\npZt0arekE6PRiGHDhmHYsGGtvlddXY2MjIwUbBXQ0NCAq666Co899piegmJMDIskSbd5i8kOGWLV\nS7HXJFlDEdUYpvQo+CZAIBCAzWaDw+HQTG8eyYtLfqQvhhfSO6Vf416vN+YN1lRVSfV6vZg7dy4W\nLFiAOXPmpGQbUoFhUUMYKuSVrP0NrnppsViQlZWV9CGTej6vqX7dKjEfMdX7RMrhkh9E8mI4Tz6l\nj3lNTY3qls0QBAHXXXcdysvL8bOf/SzVm5NUDIskSbcGqpL7G2/Vy2TQ+4doql634fNNU3ETgPRF\nziU/xGuN3t//lN7Sqc2iJkqHxerqauTl5Sn2+O2xY8cOvPjiixgyZAiGDx8OAFixYgWmT5+e4i1T\nHls2GpKMnsV0mielRMgIHmpqNBphs9mSWvUyknS7CaAkQRCk+YhyLm1CFIucS36k0zU+VdjTlXw8\n3smVjLCopmUzAODiiy9O2+snwyJJOGex/YILmqitl0nvYTEZ+ycIAjweD1wuFwRBkHVpk0jk3ic2\npPQr1pIfkRbJ9vv9AIDGxkZNLflBFAmDuT45nU7VDUNNZ+pozVJcOGdRXh3dXzFAuN1uVRc0Sbfz\nKiexp9jlcsFkMiEjIwMWi4WNkyTga7Zjoi2S7fF4EAgEYLVapRDp9/sjLvkRXmyHr3siAiBdJ5TC\nsKguDIskSbdQ0d7lQsIDhN1uV3WA0Pt5VWL/wucjZmdnsyhREun9NZtK4WEw0veDl/zw+/2tlvyI\nFCLVev1LBfZ2JQ+PdWoofdydTifKysoUe3xKDMOihiSjZ1EcopQuxEZpPMc2fO28VASIjtDzh6oc\nwSLSfEQWJaJ0E++SH+E9kpFCJHsjifQpGWFRbXMW05l2WroEQNk77uk2ZxFo+3iGz1VT61DTWPTe\nWJNrOLHL5QIA2Gw2RecjEmlRvEt+hBfZ4ZIfpCQ93wRVs2SERQ5DVQ+GRZKk49CvaPscCATgcrng\ndrt1MVctkR5UrWlvFd/gc2w2m+FwOGA2m1VxjNLxvUjaFW9vpLikUFtLfqjhPdgRer3WEiWLGquh\npjOGRY1RshGZjg3U4H0WhyG63W5pqKlelkVIx3MbTfhwYr2c47aw8UrJJueSH+yNpEgYzJNPvAmk\n5HGvqalhWFQRhkWSpNs6i8B3+ywWrBGXRcjMzNTVB5Cew2I8+yb2aLhcLvj9ftjtdlUPJ9bz+SIC\nEl/yI1pvJJf8SG8Mi6mj5HF3u92w2+2KPT4lhmFRY5R8c6bbnEW/3w+/34/GxkZYLBbNDzVti17P\nbaxgJQiCdCPAYDDAbrfDarXq9hzHwkYVaUG0JT+A1sNaxQI7kXojU7nkh9LLChClktKfJeLnOT+v\n1INhkVrRc6MyvOKl0WiUepn0TK/nMxq/3w+32y3NR8zMzFTNfMRUYK8L6UGiRXa45If+6bm9olbJ\nOuY8r+rBsKgxSrx5vF6guhro3Nmg20IoYg+T2+0G8F3Fy+bmZt3tayR6HtYYvG96mY+o5/NFpAQu\n+UGkD16vV5Of23rGsEj45hugosKK+nqgqKgzevTAf/4IOO884LzzhP/8W0CXLoCW3sPBi6tHqniZ\nLo1yPe+n2BCsq6tDIBDQ5PImFCod508nS7oNkezIkh/RQmRbQVKPN1zVKt1ez2qQjOI2XDZDXRgW\nNUaJN2hpKXD8uAcuF3DoUAOqqzNw+rQFx48bcPiwAVu3GnDiRMuf6mqga9fvAqQYKPv1C2DqVAFq\n+HwUi5m43W5pcfVoPUzp0ijVY1gML0zkcDh0M+dUj+eLSG3au+RHpBDJ3khKF0qHxerqauTl5Sn2\n+JQ4hkWS2O1A794CBgzww2qN3H3odgMnT0IKjydOGHDkCPD002ZMnizg4Yd9Ket5jFTMpK3F1dOp\nUa6X/QzuLbZYLHA4HGhubobVak31phGRDsTbGykIQsQlP8S58eL/OTdSOezFTb5khEUum6EuDIsa\no/RFsa3wZLMBvXoBvXoJAL77udpaP66+2oJrrzVjzRofMjMV3cwQ4eEhkWIm6RIWtf5hGl6YyGaz\nITc3F0ajEX6/P9WbR0RpIp7eSLfb3ao3MlpPJINkx6TD57faKH3MnU4nh6GqDMMihWjvsMzcXODv\nf/fi5pvN6N7diuJiAQMGCOjXr+XvAQME9O0ryBYiw9fNCw4PiUinsKjF/RQEAR6PJ2QNzPDeYq3u\nWyzi/vGuOZE2BPdGejweWK1WKVBGWvIjvDcy2tqR1DYep+RT8pgzLKoPw6LGKPkGfe/4e/i66mv0\nz++PId2HwGKyJPT7Nhvw//6fD088AXz5pQGff27AZ58Z8NZbRjzyiAFffmlAURHQv38AAwYIKC8X\nMG9eABkZ8T+HeNfW7XbLsm6eHoNGJFqbmxk8H9FkMul+DUwi0q9EiuxE643kkh+R8YZa8ildVMjp\ndKKsrEyxx6fEMSxqkFIB51zTObxx+A18eu5TnGg4gdK8UpQXlmNg54EYWDgQ5Z3L0atTLxgNsS8S\nNhswcKCAgQNDt9HnA44caQmQn39uwOuvG/Hb35rxhz94MXly7P3x+Xxwu93SUNOsrCyYzR1/+aZT\nWNTCfoYPKc7Ozm7zPGtl3xKl12VsiPQukfdtIkt++Hw+6etc8oNSRenPJafTyTmLKsOwSJLL+16O\nS3te2rLGjc2EQ1WHcPDcQXx69lM88/EzOHj2IKqbq6UAObjLYAzsPBCDOg9CoaOwzcc3m4E+fQT0\n6SNg9mzgl78E3nrLiBtvtGDixAB++1sfgq8P4UNN7XZ7u4aaxqLXoBFOzfsZqXpte84zgxUR6UUq\nlvzQIl73ky8ZBW44DFVdGBY1SMmGvzhcMcuShWFdh2FY12Eh36911eLguYM4ePYg9n+7H699/hoO\nnj2ITEsmBnUehEGdB2Fwl8EY0mUI+hX0a3Mo64wZAezZ48Hy5SaMHGnF//6vD1dd5YPH0zLU1Gg0\nwmazdWioaVv7K96p5QdOconVa91uNwDEVb02Ep43IkonXPKjhVpvgOpdMgrcFBa23QFBycOwSCHE\nst/R5NpzMbbHWIztMVb6miAI+KbuGylAbvhyA3773m9xrO4Y+ub3xZCiIRjSZYgUIvMzQu8YZWcD\nDz/sx9y5Xtx8swX33mvBoEFGDB7swODBBgwcKKBXL0GRJTnSpZCImnoWA4EAXC4X3G43zGYzHA5H\n3NVro9HjkE01nbNkS+d9V5re3idqlKpj3N4lP4J/T4u9kVrYRr1R8pjX1NSwZ1FlGBY1SMk3aXsa\naQaDAT1ze6Jnbk/M7DNT+nqjpxEHzx3EJ99+gv3f7sfrh17HgW8PINeei2FdhmFo0VAM6TIE5fnl\n6GLtgvJyAdu22fDVV3Z89pkJBw8a8Mc/GnDwoBFnzwL9+rUUxRk0SMDAgQGUlws47zygo4ejrYCs\nB2pofItLX3i9XlitVuTk5LS6M05ERPKLpzdS/JtLflAsSt8McbvdsNvtij0+JY5hkULIGSoyrZm4\nsPuFuLD7hdLXAkIAX9d8jX2n9+Gjkx/hqQ+fwsGqg/AEPBhaNBRDuwzFsK7DMHzqcFx9TRlMxpYP\ntvp64LPPDDh40IBPPzVg0yYzPv3UAJcLKC8XMHx4AMOHCxg+XED//gISqX2jhiCltFTtY/C800Ag\nAJvNBofDIXslNT2eQz3uExGpSzy9keLfalvyg73kySd+Jil13JV+fGofhkUNSkbPolIX4YA/gCJL\nESZ3nYzpxdNhs9lgNptxpvEMPj7zMT4+8zHWHV6H+7bfhzONZzC4y2CM6DoCw4qGYXjJcCwY2f8/\n8yBbFmI/exY4cMCAffuMePttI373OwNOnDBg0KCW4DhsWEuIHDQoeoBMh0Z5svdRnI/ocrlkWeKk\nLelwDjuKH75EytNTY1fsjQwn7mM8S36Eh0g5jwvDYvIl65jzvKoLwyKFEC/mcl4QwhdWj9S7VJRZ\nhGm9p2Fa72nS12pcNfj4zMfYe3ovNh/ZjId3PYxjdccwsHAgRnQbgRFdR2Bk15EYX9EfkyZ991Ku\nqwM++cSAvXuN2L7diMceawmQF1wgYOzYAMaODeDCCwVkZX23zwwa8vD7/VLRGrPZjMzMzA7PRyQi\nIvUQr+fxFNnx+/1SiAxe8iPS2pGkfkq3lbxeL6enqBDDogYpfVGVKzwFFzJpz8LqneydUNGzAhU9\nK6SvNXgasO/MPuw9vRf/PPpPPLzzYZyoP4HBXQZjZNeRGNGtJUCOHdcXF1/83T5UVwM7dxrx3nsG\n3HefGR9/bMCAAQIqKgKorDShd299h0Wle4zFpS+8Xi9sNlvS5yPqMfDLvU+8C09ESkt0yQ/xa+HB\nMZ4iO7ympYbSayyyuI36MCxSKx1ppAqCAJ/PJwUHuQuZZFmzcPH5F+Pi8y+WvlbrqsW+M/uw5/Qe\nbBCP7kkAACAASURBVPxqI+7/1/2oaq7C8KLhuKD7BRjVbRRGdhuJGTN6YOZMAwA/XC7go48MWL/e\niMmTczFrlg+/+pWA0lJZNlN1lLi4h/cY2+12ZGZm8sObiNIWA0x08S75Ed4jGW3JD0o+pV/fDIvq\nxLCoQUp/EBmNRmkCe7xSGRxy7bmteiDPNZ3DntN78MHJD/D8J8/j1n/cCqPBiFHdRmFU91EtIXLk\nKIwbl4ubb27AU0/ZMWGCDdOnB3DnnX707auvXipAvuUlAoGANNTUaDQm3GOsBPYsxocNWSJSm0R7\nI4OL7ACAy+XS5JIfWqT0Z0h1dTXDogoxLFIriTRSw+eoqSE4AEChozBkDqS4FuRHpz7CByc/wAP/\negD7zuzD+TnnY0SXERh12Sj8eeE4vPvqEEyZYsOkSQHccYcfAwcKHV6aQy06Gj78fj9cLhc8Hg8s\nFguysrJgTqTsrIL0GBblFDwXmYhIK2L1Rnq9Xvh8PphMpriW/ODcyI5jz2J6UkdLj1SlrUalONTU\n5XLB5/NpYs284LUg/6v/fwEAfAEfDp49iB1Hd+CDUx9g9Sercdx2HIN/MwynTo3GtFvHwfXlGPQ7\nrzP69BHQp4+AsrLv/nTqlOKdSoLwc22z2ZCbm8shQBoS3BMMRC53r8YGFIOtMti7rCwe3+QILrJj\nsVhCvpfokh9qvg6qjdLXZfYsqhPDogalqsCNuByC2Oi02WzIysrS7AXWbDRjaNFQ9O/UHwvLFyIr\nKws1rhp8cOoD7DqxC/aSldh94gc4Y8qDzTgatbWj8cE/x+DcH4biyy+syMgARo4M4LLLWv50757q\nPYotkZ6lSMOK1Xyu9dhrJndPsM1ma9WACp4TlMr10sKp9XVGROoR7foYa8mP8PmRqVjyQ+uUPBY1\nNTUoKytT7PGpfRgWNUrJxrHRaITf75f+H9zoNJvNcDgculoOIfhYdrJ3wtReUzG111QAQEAI4FDV\nIew8sRO7TuzCrq6rcGzAMYzsOhKDc8fAdnYsNm8di2XL8lFaKuCyywKYNSuAQYPUN3w1nteM2Avl\ncrnaVcGWUk/sCQ6vTOvxeCIGwPA5QRzKRURakci1KDj0ccmP9hGPhVKcTicKCgoUe3xqH4ZFasVg\nMCAQCMDj8cDtdkvDD9U+1LS9YoUoo8GIAYUDMKBwAH4w9AcAAKfLiV0nduH9E+/j/dqHsGfIHhRf\n3BNdjGOw46txePr742Fu6IXZswKoqBDQu7eAkpLv1nVMlVj7KVaw9Xg8sFqtyM7OVs18xHike8+i\nOFy4ubkZfr8fdru91VqmsZ4n3vXSxCAZXJCCQ7mIvsNhqMkjZ3BJ5pIfWsYCN+lJO61BCqFU41ic\nNC42CtU+/FAOiR7LPHseppdOx/TS6QAAr9+LT779BO8ffx/v569DoNtdaPYasNU1DlvWX4zmQxfj\n9CdDkJ1pwtChAi6/3I/ZswPo1k2pPYosfD/Fc+1yuaSAoeX5iHoLi/EIHi4MAHa7HVarVZb3a7TG\nU3iIFF9HkYa0pvMdeCLSh44s+RFp2Q8tXwuTUeCmsLBQscen9mFYJAChQ03Fi2JOTo6mL2rx6mjw\ntpgsGNltJEZ2G4lbLrgFgiDg69qvsePYDrx3/D3sOPYEbFecQXnhRShwX4w3PhqPZfeORr9SKy6/\nPIArrgigT5/kBB3xw00camowGGQNGKmix57FWARBgMvlSsnyJYnegeeQViJSQqp7cdu75AdHZkRX\nU1PDnkUVYljUKDkuKOE9S2KlS0EQUF9fnzYXLbmDhsFgQO9OvdG7U29UDq4EAJxtOov3jr2HHcd3\n4EvzYnj7fI5G20j89eQEPLSoAl29F2HOZRm44ooAhg5Vbr6jx+NBc3MzzGYzMjMzdTP3VBw6rSeR\nXpeBQEAKiYkuX5KMQN2eIa1A6+qE4s8TaU2qAwypQ7zXwvCRGWq/qab069vtdsNutyv2+NQ+DItp\nKLiUfqSeJfGilS6S0Yju7OiMK/pdgSv6XQEAqHPXYeeJndh+bDu2D7gb+059guc8g7HyoQoYj07E\nqC5jcMHQLIwYIWD48JZKq+29PosFT8ReY73OPdWz4KI1WliqJlw8Q1rFv4MbTk1NTbobxkVE8tBi\nMI+nN1LNS34oeczFdpjWzmk6YFjUqPa8mYKLmMTqlRDDkxYvxB2RzP3NseVgWu9pmNZ7GgCgyduE\n3Sd3Y/s32/H24d9i29mPcMA3EC9vnIjqBybC9u04jByUieHDWyqujhoVO9wG9xoHAgHYbDbpbp2W\nQka89DoM1efzob6+Hj6fL6GiNVoRreEkDosXl/sIBALw+XwRi0oE/xEfk4hIa+Ra8iM4RMp5PUzW\nZyyv4erDsKhz7Slikm5vVPGCmspw7LA4MLHnREzsORF3jwdcPhd2ndiFbd9sw7YxK/DRqT340jwQ\nzvoKPP2LKRjSaSz+504bxo4NvXjHmo8ovgb0SE9hUSxaI65n6nA4dF9kKhK5hrRyLlCodLsJmGw8\nvsmTLsc60SU/Yl0Pg9eOTJR4vJU65l6vV5c3s/WAYVGj2nqzBg81NRqNsNlsCRUxMRqNCAQCafPG\nVVvYsJvtqOhZgYqeFQCAZm8zdp/cja1Ht8JYci/+deJjzPjLCHR9fhJ+etkE/HDaCAg+oc1eYzXt\nI4UKDvpGo1EqWGOz2VK9aUkX6/3Y1pDWaHffIw1n5ZBWIu1Kl7AYSyJFdqL1RqplyQ+n08niNirF\nsKgzwXObEi2AEUxt4Ulpat/fDEuGFB7vAdDgacC2I+9h1catuOvdX+GOjz/H4E4XYO7wSbik9BIM\ndQxt9Rh6/lBV+/mLJbhojdlslt6zeu4JVkJbd99jVSaMduddz+8ZItK3RJb8EIf5x1ryIxnLZjAs\nqhPDokYFv2GDh62J89M6OrdJy43v9tDS/gqCAItgwbiiizB24YUwm5fhT2+4sOLlHVh58J9Y3feH\naDJ8i4qeFZhcMhmTSyajd6femtrHdOD3+9Hc3KzZojVaksiQVvHfAIe0UuLY25Uc/Cxrv/Yu+SES\nR7/IfU2srq5mWFQphkUNE4eaulwumEwm2O122dZaS7dgoYX9DT/fwWvr/WiBHT+89jK8/vpsPPqo\nCacaTsJ71Tt42/UOVuxYAbPRjIriCozvNh4zB8xEoUNfi95q4fwBLR/EYu9/W0VrlFjShUK1dwgX\nh7QSqQPfc/KKdWPN6/XC5/NJvYxyXxPZs6heDIsaVldXB4vFguzs7HYNNY1FnLOYLtQcNsTKkOJ8\nxGjn22QC5s0LYN68APbv74Lnn1+AV+5YhL79Arj0e5/C1OkfeO2L17B422L0yeuDKb2m4JKSSzD6\nvNGwmbU9L07N5w/47oO2ubkZgiDAbrenZdEaLYnVaApeIy3akFa1zAMi0iP24CZX8BB/q9Ua8r22\nromxqrUGU1vP4g9/+EOsX78eXbp0wf79+1O9OSllaKOBpd7WF0nVEpXQ1NQEg8GAjIwMxZ5DTRob\nG6XeWTUI74ESl75IdGixxwNs2GDE888b8d57Rkyd6sL4iQHYSnfiS7yNrUe34POqzzHu/HG4pOQS\nTOs9DWX5ZZr7EPb7/aivr0enTp1SvSkhwovWJNL773a74fV6kZWVJcu2+Hw+6a6w2gUCATQ3NyMz\nMzPVmxK3SPOAxMZT8DygVA9pbWxsREZGhiZeB1okjvywWCyp3hRd0+I1Qus8Hg8EQYi76FqkdXSD\nr4vHjh3D3XffjbKyMpSVleHEiRPo27cvrrvuOlW0QbZv346srCwsXLgwXcJi1IPOsKhh4htXCWIP\niMPhUOTx1UYt4Vicf+pyuQAANpsNNptNlgvn8eN+/OUvPhw4kIkPPzTgxAkDhg4VMOjCs7D224JT\njk3Yee5tmI1mTO01FdN6T8PEnhORY8vp8HMrLRAIoLa2Fnl5eaneFACti9aIITER4jzk7OxsWbaJ\nYTF1IoXIWGukKTmklWFRWQyLyeH3++F2u9OmjaIGbrcbBoOhVc9iewiCgNraWmzduhWHDx/G4cOH\nsX//fnzzzTcwmUzo169fqz99+vRJ+g39I0eOYPbs2QyLDIvaFT7pWE5iJUa9NNbakupwHClcmM1m\nWRuM4YGqpgb46CMDPvrIiA8/NODDD41odgnod/FBZAzaiKq8TfjKvRPDuw3D1F5TcWnvSzG0aKgq\n7viFU0tYDB4ybLVaYbfb2120hmFRP2Exmmh33ZUc0sqwqCyGxeTw+XzweDwMi0mk9Gv7Zz/7GW65\n5Rb06NEDhw4davWnsrISS5cuVeS5o2FYbME5ixSR0WiE1+tN9WYkjcFgSMkczeClTpSuiBk+r69T\nJ2DKFAFTpny3PMPJk8Devf3x0UcDsGfzz3HyYxc+6/kumi95C8/uXQCP0NgSHEsvxZSSKehkV8ew\nz1TPWfR6vSFDhnNzc2VpjKt5HiZ1nDgvMlykIa1ipdaODmnlXC9l8fgmD49zciVj6YzOnTtLfy6+\n+GLFnosSw7CoYUq+aVPd+E62ZO6vWOxE7L2NVRFTqeeP9trp3h3o3j2Ayy4Tf9aMgwcvwZo10/DK\nk79H39GHgYwNeK7+edy44UYM7TIU00unY3rpdAzqPCjlH97JbKgFn8dAICB70ZpUH8tUSrfrTzg5\nFtpmlVbSM4by5FP6mNfU1KiqwA19h2GRIkq3xloy9je42InBYIDdbofVak3aB57YAE3kgm8wAIMG\nCXj4YT9+8xs/3nijF5599lZ89tlt+P5/N2DAqH/iQP1GzPvrPPgEH2aUzsCM0hmY2HMiHJbkDQ9K\nZqMh/DwGL2GiZmrfPopPImtGRqpICLSMaDCZTKzSSkSq4Xa7VVNkkEIxLGoYexblo+T+ihPxxfmI\nmZmZss9HTAa7HZg/P4D58wP48ksDnnsuA/dWzkYgMBs9SwIo6PsZDp1dj3/u/z+cCCzCqC7jcEX5\nDFzebwaKc4sV375Eg3Cigte5TMZ5TLf3IHVMtN7I8BAJtAybFgukReqFZG9k+7HHKzl4nJNPyWMu\nftap6Zxee+21ePfdd1FVVYXzzz8f9957L37wgx+kerNSggVuNMzv98Pn8yny2IIgpNUCqT6fD42N\njcjNzZX1MYPnI3ak2IlcampqkJ2dLdt2BALAmTPAkSMGHD1qwJEjLX8OH6/BF/63UZW/Hih7C3ZP\nD/TyXoZR2bMwvnQEZkwHCgpk2QSJ0+mUba5gMDmL1iRC7tek2NOkhcImgiCgsbFRtmVD6DsNDQ3I\nzMyUbkaopUqrXjQ1NcFms6X8Wq93iS7jQB0XfO2QmyAImDFjBnbs2CH7Y1PcWOBGj5LxoZ0ud+/k\n6sUJn8dms9mSOh+xLXL3VhmNQLduQLduAsaMCX7cLABXwue7EkeP+bDx4C784+v1WNfwQ7zy7xoE\nbr0M5abZ+EHFRMybY5clOMq9bz6fD83NzbIXrYkXexZJaR0d0prqNSMpfaVL20QtlP4s8nq9vMGi\nYgyLFFF75rdpWUcb5uIQRbfbnfDi68mU7ABiNgOlvcy4udc43IxxAB7Al9Vf4m+frsfLHz2Kxacr\nsfjOSegbuByLxs7AgisL2h0c5dg3pYvWEP1/9s48Torqav9P9d7T3TMMDCCbrAOyg6C8KC5EZHPF\nCNFoRKLRuKFxiTGBxKgxEX3zGqPGmMTE+L4uP41oNKLGXUkMuEREFkEB2bfp2Xp6qe33x+Q2NUXv\nXbe7lvP1M58ZBqmuqlvLfe455zlWoJCUVvZda7CTqdWH06KRTnlnEs6CXde8rm0nZbJZERKLFob3\nC4m1kzBLVIwnTGgU+6LXpih6vV6Ew2F4POa9rcwQrRrWfRhumnYtbpp2LZriTXh+3cv44z9fxI/2\nXo8f/mQchohn4ZR+p2NQ7TBEIipqa4HaWqR/PvS9U4waQbXNhwjCChTj0ipJUvp3lNJKGA1bnCDs\nAYlFc2PeWS1RdVwuV9WFRaUoZtKiqmq6HrFaKYp2oXuwOxZN+iYWTfomElICL298Cw+//SIea/lv\n+Nu7o/+es9Cw/2y49k1Ce5uAtjagtbXze1sbcNxxKi65RMbZZyslCeFKm9YUg9HC3gzHRNiXUlJa\nAZTVM5JwLhTBrSy8z3dTUxOJRQNYvnw5brvtti6/W7NmDV566SXMmjWr5O2SWLQwlYgsOkUsAvnd\nNFVVRSqVQiKRgKqqlkxRNPOYBjwBnD16Ns4ePRuKeh9W71qNv37+Vzz/+QVIykmcNfwsnDn8TBzf\n/3i4XW6kUsCLL7rwyCNu3HijB+ecE8KllwLjxuX/LH1EOBKJmDoiTBBGUA3HwXwprVohaYeUVhIx\nhB0hsWgN5s2bh3nz5qX//PDDD+OJJ54oSygCJBYtD8/Jv5mFBQ+ypd1qo09ut9syffUyYZUxdQku\nTOk3BVP6TcEdJ9+B9QfW4/nPn8fNr9+MHW07MHfYXMwbMQ+nnTkd55zjx5YtwMMPA2edFcDAgcC3\nvy1j7lwFDQ1dt6t1qDV7RNgqY8UTmnjbF230MFM0UpvSqjfYyRaJpGvFOdCzobLwPt/RaBQ9jLZI\ndziff/45br/9dvzzn/8se1vUOsPiMPtoHsRiMbhcLgSDQS7bNxstLS2oqamB1+sFcHj0KRAIWD76\n1NHRkW4kb1W2Nm/FC5tewHMbn8O6A+swa+gszBs+D8f1Pg413lq8+WYQjz7qwttvuzBwoIoTT1Rw\nwgkpTJrUgUhEht/vRyAQMP1Ew+j2NYqiIJVKmVYc6+Fp0+5UrN6SRB+J1H4B1U9pZeeXrlv+UIuS\nysK7Vcmvf/1rNDY2Yv78+Vy27zREUcTUqVNx8803F3NOqXWGXeEZfXBSzSJwKLKYSqWQTCZtWY9o\nh2jVoG6DcM0x1+CaY67B7vbdeOHzF/Cbj36DS3dfilMGnoKvj/o6/vh/c+BDCKtWyXjjDRUPPujD\nRx/1wPDhKk4+WcFJJ6k47jgFkUi1j4YgiELJldIKoIt41Ke0ZotI8tpPgi8UWbQXFFk0lqVLl2Ls\n2LGGiW8Si0RWmHhyAmzFuqOjI936wmr1iIVidbGopU+4Dy47+jJcdvRl+OrAV3h568v485o/48oV\nV2Ja32k4q/EsXH3DmVi6tB6pVAqrVwt46y0X7rnHjY8+8mDcOBXTpyv42tcUHHusCp+v2kd0CHbt\n0aSIIHKjTWfNldKqqmrOlFb2Z0ppJYiuUM2idXjrrbewfPlyfPTRR4Ztk8SixeF589ohCpUPRVGQ\nSCSQTCYhCAJ8Ph9qampsO1Gw63EBQPdAd5w3/DzMHzofMTmG13a8huWfL8f33/k+pg+cjnOOOgdz\nj5mLadMiWLJERkcH8I9/CHjzTRduusmDzZsFHHecggsvVDB/vj0XSew8/gSRiWJcWpmg1BrskEur\nOaFFtMrCu1VJNBpFg95kgCiaaDSKRYsW4cknn0QoFDJsuyQWiazYObKoNTrx+Xyora1NC0Y7v4Ds\nuADAxjKVSsHj8aC2thb17npc3HAxLp5wMaKJKF74/AU8vvZxXPPKNZg+cDrmj5yPOUPnYMaMEGbM\nkAHIOHgQeOstF2691Y2VK124+24J/ylfrRr5HHoJgiiNYnpGalNac/WMpHu1MtjtHWYFeF/bzc3N\nFFk0gIceegj79+/Hd7/73S6//+EPf1hWSioZ3FgcSZIgyzK3bcdiMdTV1XHZfqVRVRWiKCKRSEBR\nFPj9fvj9/vRkIR6PQ1VV1NTUVHlP+cHqMSMWL9ZjvS7j8ThkWUYgEEinleUav2giir9+/lc8s/4Z\nrNq1CjOHzMT8kfMxc8hMBDwBAEBLC7BokQctLQIef1xE796VOqoM+xuNGlYzyya9VpnMksGN8Vjd\n4KbaMBGZyWSHiU9FUeDz+SgayRG6jisPb0Oh2bNn491337WNP4RFIYMbu0JpqPlRVTXd+kIQBAQC\nAfh8vsPOnZ0jqQyrj6m21yWALmPJxH4u6gP1WDhuIRaOW4j9Hfvx3Mbn8MAHD+Cyv12GucPmYsGo\nBThl0Cl45hng9tvdOP54H558UsTkydY9ZwRBGANLadXDUldlWUYymYSiKJAkiVJaOUERXHtRjf6v\nRHGQWCSyYnVhwV7cyWQSHo8HoVAIHo8n6wPJ6sdbCFY9RlVV07WlrJ2LvtdlsWK/Z01PfGfid/Cd\nid/B7vbdWL5hOX7xj1/g0hcvxbyj5mHBogUYN/4EnH22DwsWyJgyRcXkyQqGDAEq9U4zcrzoRUzQ\nJJsPTPgxYRgIBNJ/V2pKK0GYiUo8O+i6Ny8kFi1OJSKLVptgiKKIZDKZbrxeW1tbUOqEVYWUndEa\nEHm9XoTDYS69LvuE++DKyVfiyslXYmvzVjy9/mlc//fr0ZRowhn3LQC+PA/PLj8aP/yhD/E4MHly\np3CcPbvTRZUgCCITxRjs6F1aM7m1WuldzAurzUnsAM9zLooi9cs0OSQWiaxoV0vN/mDWpieqqopA\nIFB0vZMTxKJVjjGTAVG+l4lRxzao2yDcNPUm3DT1Jqzbvw5PrX8K/2/fefB+zYtLrjkPX2s4D/s/\nH4ZVqwQsXOhFr14qrrlGxtlnKzBaxxo9Xla4lxlWefYQRCnk6hmpb/eh7xmZrd0HQfCA95whGo2S\nuY3JIbFocSqRFmBmcaEoSjrVNFt6YqGY/ViNwMzHyExrEokEJElCIBBATU1NwQXvPI5tVM9R+GnP\nn+LWE27Fql2r8ORnT2L+hydhaP1QnD/vfLz1/a/jX2/2wq9+5cYtt3hw5ZUyFi2S0a2bobthGDSh\nJAh+GLG4wcOl1W7QIlJlYeeb1zknsWh+SCwSOTGruJBlOd0uwaj0RLMeq5GY8Rj1UeFgMIhwOGyq\nyYAgCJjSbwqm9JuCZacsw+tbX8fjnz2OH7/9Yxzf/3h89/7z0b/9DPz2gTBGjvTh/PNl3HSTjD59\nqr3nBEHYhVJTWjMJSUppJcxCU1MTiUWTQ2LR4lQismgWh1B95Mnv9xvWVgAwp5DihRlWZrUuteVG\nhYHKjZ/X7cXsobMxe+hstCXb8NdNf8Wjax7Fh7sX48wFZ+KBxRfgX//vJEye7MN118m45hoZGr+L\nonDSNUkQRGkYkdKqFZTVfjfkwwzvLyfB+3yTWDQ/JBZtAM8JpcvlqvpkNVM9Io/IkxMm5mZ4wWpN\nazweDzfTmkoQ8UdwwZgLcMGYC7CrbReeWvcU7vz4erQe2YqvP3g+3nj6IjwycSTuukvCGWcoFXNR\nJQii8phNxBST0irLcvp3Zk9pNdt5tju8z3c0GkWPHj24bZ8oH+p+SeSkmgJKURTE43E0NzcjmUwi\nGAyirq4OgUCA64PLCYKxGscoyzLa29vR0tICVVVRW1uLSCRimFCsttjvG+mL7035Hj645AM88/Vn\nUBNJYv2UU+C9cgoW//lhzDijHS+84EIyWfg2q31MBEHYE5bS6vV64ff7EQwGUVNTg1Ao1CXLg7Wg\nisViaG9vR0dHR7oERJKkdJSSsC+8xWJzczNFFk2ONZfziS7wnFBWY7IqSRKSySRSqRR8Pp+hgiIX\nVnJ/LYdKjmm5pjXFYCZhNa73OIzrPQ53nHwHXt/yOv7c/3/x0uc/whVvnIrEnRfj7LEz8I35AqZP\nVw13UCUIgiiVQlJa2fdMKa2Z2n0Yjd3f0WajEmmoFFk0NzRNIXJSqZpFVkuRSCQgyzICgYCh9YiF\nYibBwYtKHCMbz3g8zjV12Ox4XB7MGjoLs4bOQjQRxTPrn8Ejo2/H8wcvxWtPX4DkjRdj/kkjMX++\njOOPV1Hhy51wGDTJ5oudz28xKa2SJOVMaWXbsuu5IoqD0lDND4lFG8DzgetyuSDLMrfta01OBEFA\nIBCAz+er2kuExGJ5GG1aUwxmH7v6QD2+M/E7+M7E72DjwY147NPH8OfRs/C3eD+8+OtFUL9zPhac\nFcb3vifjiCM6/43Zj4kgCKIUl1YAWesi870vWCSTqAxUs0jQ3UbkhNdkVVEUdHR0oLm5GaIoIhQK\noba2Fn6/v6qrjU6ZnBt9jNnGs5rC38yM6DECd5x8B7ZcswkPzl+C/zr/NbRdOggv1yzE+LPfw28f\nBkxiQlw1nHIvEoRdYVFFj8cDn8+XLkMIhUIIhULw+/1wu91dMlFisRg6OjoQj8eRTCYhimLafIeo\nDlSzSFBk0QbwvImNnrCx+jVRFOHz+VBbW3vYamQ1ccIE1cjrRdvvstrjacWxc7vc6TTVAx0H8NS6\np/BQw/fw/R1tWHbpIty78FycOqVf2Z/DHIWTyWRFaooIwonYOQ3VSNg5yhaN1Lu0antGulyudGSS\n/ZlSWvnC+7pOJpMIlNpfiqgIJBaJnBhRs6itR1QUBX6/n5vJSblYUXAUixHHyMaTR7/LcrHqhK2h\npgFXTb4KV066Eh/t/jduefpRLHjzBBz59rH46VkX4+tjToPX7S1qm9q2MwDSq/j5aopIRBIEUQ0K\nSWlNJpPpZ1u5Ka1EfnjOidi2aZzMDYlFG8C7ZrHUB4XZ6hELgcRidvSi32ymNWbZj3IRBAGT+k7E\nq9dOxPrNS/DdX72KS373IC7vfS1OrLsAN596MaaNHJ5zG/ra0ZqaGrjdbkiSdNj/l62miEQkQRBm\nQWuwwzJZmKDURyO1Lq30HDMG3ueLxsPckFgkcsKERTHRGm1qotfrtVTTdRKLh6MX/ZU0rSkWu7U+\nGdi3Bi8vm4e2tm/iz3/bhMc+exSnPn4qauIjML32ElxzytmY9l9+sEV4tuqeSCTg8Xi63HuZ7uNC\nbPIzichcDocE4VTIeKUyZHqO5UtpVVU162KY/md6jnWF5ztVFEXLzA+dDI2QDeBds1gI+n56fr/f\ndPWIheAEsQgUllaiFx6hUAgej4depFWgVy/gxkWNuBF3oCP5Y9y74m94dO0fMPe1G+C970KcdsS3\ncdOiIzFwYBxer7fse69QEam1ydf2WiMRSRBEtSnUpZWeY7nhKRaj0SiZ21gAEotEXlhBeabJyFov\nIwAAIABJREFUp7Ymyg799CrVV7Ka5BPEZjKtKRa7if1Mx1Pj9+GHZ8/DD8+eh80HN+N/3v4Dntxw\nKv76yHAcFbsUt59/Nmadkn28ynnxF9NrLVPDbpp8EQRRLuWKl1KfY05MaeX9Po1Go6ivr+f6GUT5\nkFi0AZXIJdc/MLRRJ7fbberUxGKwm9jIRDZBLEkS4vG4KU1rCsUJ4wccchXu4eqBu2cvxS/PuBXP\nb1yBn7/6B3z9vRtQ//hFuHbaJVh8wVD4/Z3/hk2QeJ2fQlLBsolIcmitDHZK0TYjdH75w/v5nu85\nxr5nSmnN9Byz+vXA24CmqamJIosWgMSiTeA9CWTb1tcjRiIRW+WbO0FsaI/R7KY1xCH0qd6BQACh\nUCg9VgvGnI0FY87GF01f4MfPP4Lbtp+M228Yj7P7fwe/vGwuGroX56RqFIWKSEmSuqzgs2tTURQS\nkQRBdKHSzwL2HNOTKaVVluWsWRVaYWkVeO4riUVrYJ9ZPsEVM7dKMBKniEVFUZBIJCzlVFsIdhs/\nQRAgyzJSqRTi8XhBqd5Duw/F/y36GZLSj/Hr15/Dr1b+GgN+eR2mBhbhv8//Fkb171vho8hMvnqi\neDwOAOTQShCEabF7SivvaHk0GkWPHj24bZ8wBhKLNoHHJJnVI8qyDFmWEQwGbR91spvY0KMoClKp\nFCRJgiAIZFpjYlgkURTF9P1XTKq33+PHjbO+gRtnfQOvfLQONz/zexz32HEY6j4RP5l7Kc4cc6Ip\nx107+fJ4PIe5uRbS5kO7em/GYyTsCaWh8sdK57hQgx0zu03zPt/Nzc1obGzktn3CGEgsEofBok7J\nZDI9WXO73QgEAtXeNe7YVSxq04fZyysSiVR7twzHDuOnbVUCID1W5bywZx09CrOO/iU+Wb8E3/vj\nX7DwiVtQ2y2Fq469BJf/1/noFuhm1O5zo5g2H+xngJp1E4SdsJJYzEahzzJtKr4+pVXf7oMXvM93\nU1MTRRYtAIlFm2DEzczqoURR7OKCydLfnIAdxIYW7Ziy9GFFURCLxaq9a1yw8vhl6pHIVpyNelmP\nHBrGitsvwq5dC/GD36zGsid+h7s/+DnOGDIPN55wGUb3HG3I51SSQiZe7Ds5tBIEYVaKSWnV1kXy\nTGmthBsqiUXzQ2LR4WgNTmRZRiAQQE1NTZeHlRPaSTCY2LDy6qXetMbv93cxQmHHR5gDbSRf3yNR\nlmUun9mvH/DYHcdg//5jcc9DB/GnJ/+Ev206ByN7DcX1x1+O04adBo/L2q8HavNBVBorvzesglPP\ncSkprYAxmRVUs0hYezZApCn2ZtamuuUzOHG5XBBF0ahdNTVWfglpe14CyDqmVo6+5cNKx1ZIP0uj\nj0e/vZ49Vdy1tDt+1Ho9fvfI93Dv//sbrtl2P77X8ANcccwluHjsQvSs6WnY55uFUtp8WMWQgiAI\n51BuZkW+tkWVqFkkN1TzQ2LRYciyjGQyma5HLMTgxEoTcCNgx2uVSaC+52VNTU3OMXXaeJqNTKnB\n1XYWrq0FbrhOwFXfPR1PPjkPd/35M/xm8wO4Z+UkzB58Gm44/gqM6zWuqvtYCQoVkeTQShDVwUrv\n5mpSTGaFJEnp3+mfZ4qiwO12czvvyWTSEX4YVofEok3IdxNnq0csdNtOEhdWOd5ye17a8aVr1rHL\n1yMx37+tFIEAcPHFIr71reF49dX78dQLP8NLK/+IF9d/A/2Cg3DtlCuw8L/mWj5FtVhKdTU0m4i0\n4z1vJuj8ElagmOcZ+0qlUoan6LN3G90z5sdZb3yHkal2TV+PWAhmnYDzwuzHq49MFSP8Afs/mM00\nduweLLRHop5qjZXbDcyZI2POnDBSqWvw2ptX4YE3XsRNzz6Im9/4EU6quRy3nX0hRg8xv4sqT4px\naDWrNT5BWAkS5PzI9Dzr6OiA1+tNRxez1Xlne6YV+rmEuSGxaBO0NxtLS0wmk3C5XAgEAkX1Z9PD\nUhGcghkNfVhkKh6PZzUiKgarpdoWilmEvr5+tNgeiWbC5wPmznJh7qwzIYpn4o+v/Bu/+fghHPfk\neBwXWYBfX3A5hnUfVu3dNBWFikhtChiZ61gbMzx3nACd58rDnkUAykrRFwQBsVgMkUgk7YVRTDZU\nJXj55Zdx3XXXQZZlXHrppbj55purvUumwFyjRJSFPi0xHA4beiPaUVxkwiyCAyjctKZYzHSMRlJt\noa81jnK5XHnrR/NhtnHyeoHLTp+Ay05/CO99shff/s0jmPLwLEwbNBk3HHcVThhwgmHPCLMduxGQ\nQ6v9oTHhD53jypFv3ldMSquiKLjwwgvx8ccfY9iwYRg6dCiSySSef/55jBw5EkOGDKmqeJRlGVdf\nfTVee+019OvXD8cccwzOPPNMjBw5smr7ZBZILNoERVHQ1tYGn89nuGEGm5SQWKwcqqqm2ym4XC7D\nI1NmOEY7kalHotlWTI1m2vjeWHf/Lbjrlzfhgf97CpfuvRE9unlx9eQrce6Ic+H3+Ku9i5aiFIfW\nQh0NCcIusOueqAylzvuyLYy98MILOHDgADZs2IBVq1Zh8+bNePjhh7Fhwwbs3LkTQ4YMwVFHHYWR\nI0di0qRJOOecc4w6lLysWrUKw4YNw6BBgwAA5513XlrIOh17z2YchNvtRl1dHbdJgpPERTWPVd9z\nzwmiw0gqPXa5eiQagdHHY3RKuccD/Oj7Hpw+61tYsvTb+CD6Om7b/kv8qO42XHXMZbhk/CJ0D5It\nejkUKiIlScrb5oMgCKJQeL1LGxoaMG3aNAiCgLa2Ntxzzz0AgHg8jk2bNmHDhg3YsGED1q5dW1Gx\nuHPnTgwYMCD95/79++Nf//pXxT7fzNAs1Ea4XC5uN7fWQtnuVEMsluNWWwp2Ff+VOq5CeiSaEV7n\nZvx4BS/8NYldu07AX/4yHY++vB73rL0XyxonYlafb2DJqd/FUb2GcPlsp1Jqk25BENIZCxSJNA6n\nZN5UGzrPlYfX+Y5Go+jRo0f6z8FgEOPGjcO4cdVp00TXVXZILBIFYVdxkQmXywVZlrl/TqZ2CuWY\n1hSDk8bTSMzYI9FM9O2r4pprRFxzzTBs3PggHnn6Vjz77m9x7JZT0NB+IubWX4vzjj8GkyfLoNZa\nfMhlriOKIiRJgiAIWY0o9D/TBIognAlvYR6NRtG9u3kyT/r164ft27en/7x9+3b079+/intkHkgs\n2gieAsBJ4oL3sWpNa1RVRTAYLKqdghHYdTx5HFc5PRLLhdfxVGLfR4xQcNeSBtyFH2HXgWtx16uP\n4y87L8ZfVvSD9IPvY3LtbJwwTcW0aTKOOUZGMMh9lxyNVkT6fL7077M5tLJIJJnrEGaCIouVg/e5\nbm5uRmNjI7ftF8vkyZOxadMmbN26FX379sVTTz2FJ554otq7ZQpILBIFYVdxkQlex6p3yqxmOwUn\njWeplNsjkThE34YwfvXNy/Dfyrfx/Kbn8T8jbsXWtu+jJvo9vHrbt7BlUxgXXijiu99NYcAAui55\nkWnyV0ibD/adHFqzQyKGsBu8r+mmpqYuaajVxuPx4P7778esWbMgyzIuueQSMrf5DyQWbQTPm9pJ\nvRaNFlJmNa2xo1g0YuzM1CPRbqLe4/Lg6yO+jnOGn4N3tr+De1ffi109b8XCwd9F+1tX4vjjGzBj\nhoSrr05h1Khq762zMarNB9sGCSnCCEiUV45KpKGaSSwCwJw5czBnzpxq74bpqP6MlbAE1e5fV0mM\nmqDLsox4PF4x05pisOvLtpyxM7pHIpEdQRBw0pEn4aQjT8La/Wtx7+p78ff+I3D+Hxaidv1iXHjh\nQAwY4MVVVyVx+ukAlYWai1LafGRzaKX7iygGEov2wYxikcgMvYJtBM8HqN0iHLkoV3CIooi2tja0\ntramW5qEQiHTCEXAWeOZD0VREI/H0dzcDFEUEQ6HUVtbW7VoIk/MeDxjeo7B7+f+Hu9c8A4Udxy/\ndR+NU/7nUsy58DPcfXcQkyaF8LvfeRGLVXtPiXwwEen1euH3+xEMBhEKhRAKhRAIBNKLL7IsI5lM\nIhaLIRaLIR6PI5lMQhRFyLJsyWcTiRjCbjgxskhkhsQiURBOEhelHCuLSrW2tiIWi8Hr9aJbt24I\nBoOmdMu063gWc1yKoqCjowMtLS2QZRm1tbWIRCKmSBFmsBe1HcdKz8C6gbj7a3fjo0UfoXe4J37V\ndiqOvPHruG7ZP/Hmm26MGRPCT3/qw+7dNCG3GloR6fP50s7PoVCoS5q3HUUkYRw0/pWFt1hMpVLw\n+/3ctk8Yh3lmRUTZUM2iMRQjOMxkWlMMdhWLhWDVHolOoaGmAUuOX4Irxl2Bx9Y9hp9/sgCjzh2F\nZdfdiFVPT8eUKSFMmybhtNMkzJolo6HBmdexHSjEXCdTr0he5jqqCsRiQEuLgNZWAa2t+M93Ae3t\nAjweFV4v4PcDPp8Kn6/z5969FfTtS+nSlcLs71e7wGqQeW0boLG0CiQWiYJworjItaqmNa3xeDwI\nhULwer0V3sPSset45jouq/ZIZMfktJdq2BfGlROvxBWTrsCT65/EHauuwBGTj8C9F92A+Jo5ePll\nL26+OYBRo2TMnStj7lwJjY0KHHaabEmhIpIJyXwOrS0tAnbscGH7dgFffeXCzp0CDh4U0NQkIBo9\n9D0aFeDxAHV1KmprVUQiQG2tiro6FeGwClkWkEwCqRSQSglIpYBEAti924VduwT06qVg6FAVgwcr\nGDJExZAhCoYMUTB4sIJQqEon00Y48TlYTSpxvmk8rQGJRRtBNYvGwCYqmR6UFJWyBmzsqtkjkTAG\nv8ePhWMX4oLRF+C5z5/D3at+ArdwG25YegN++/BZWPmeFy+95MGZZwYRDAJz5kiYO1fCf/2XDBNl\nFBMFkEwC77/vRlub8B9BBohipzDrFHydom/HDgG7dgkQRQGyDCgK0t+BzgifIHR+V1XA41ExYICC\n/v0VDBigYsCATiHXowdQX6+ie3cV9fWdX4FAafve0SFi2zYVu3YF8eWXLmzZ4sL773vw5ZcubN3q\nQn39IfE4aJAKUURasDY1CYjHAa8X8Hg6v7xeFaoqIJHoPC/JZKdQFUVg4EAVY8bIGD1awdixCoYN\nU4q61js6gGAQtLBCVA1RFE1V8kHkRsgjAJyhDmwCs/znte1oNIr6+npHTLSbm5sRiUTSQlAUxbTg\n8Pv9CAQClohKZYP1D6ytra32rhhOU1MTunXrBkmSuvRI9Pv9lrx2o9GoYVFQls5nhWs3mUxCEIQu\nDeSBzmfRy1++jLv/dTfaUm244dgbcO5R58IteLBmjQsvveTBihUebNvmwhVXpHDjjSkSjf8hlUpB\nVVVT1QmlUsCbb7rx7LNerFjhQWOjgl69FPh8neLJ5+tM+QyH8R/Bp6J/fwV9+6rweCWk1DiSShyi\nmkBKSSApJxEX44iLSSTlJJJSCqoriZScREJKICklIcoiREWErMqQVRmSKnVGLKFA/c9/siJDUTv/\nDCD9nSFAgEtwpb+rqgoBAvxePzwuDzyCB26XG26XG17Bh442H6IH/Gja78fBfX4EPH7U1/rRvdaP\nhjo/IjV+eNQgXHIQLrkGHjUEt+BBIKDC7wf8/k4h63YDW7a4sHYt+3Jj1y4Bw4crGDNGwZgxMsaO\n7fzevTtw8CDw8cfu/3y58PHHbuzf3ymy6+pUdOsGdOvWKT5PO03C9OlyyYKZN6ymtaamptq74gg6\nOjrg9/u5LIjv3bsXN910E5YvX274tomSyTpBIrFoM5LJJLdtGzlpNTstLS2oqamBqqpIJBJQFMXS\ngkOPJEmIxWKoq6ur9q4YClvUYOlnVqkhzYV+4aIcFEVBKpWyxD2cTSwyVFXF29vfxrL3l2FH2w7c\ncOwNOH/U+fC5O///rVsFXHddAG1tAn73uziGDKHXWb5zypuOuIytu9uxZXcrtuxuw1v/bMPKD2M4\nYmArxk6OYtioFiDQirZkG2JiDDExhvZUe5ef41IcHWIH4lIcKTmFGm8NAp4Agp4g/G4/Ap5Al+8+\nt6/rl8sHj7tTzHkED1yCC27BDRdccAmu9Hcm9Nwu96G0WKHzvlHRmQ6rQk0LypSY6vxZ6PydpEiQ\nVAmSIkFURIiyiJScQkpJISV1fk9KSSTkTgEbl+JISAnEpTjiUhwxMQa34EaNtwYhbwghbwhhXxhh\nbxghXwhhbxh1/jpEfBEEhFrEmuoQ3V2PfV91w87N3bFlfQO8Uj2UjnpMGOPFxIkKjj5axsSJMgYN\nUiFJnbWZ0SgQjQpYvdqNF1/0YO1aN844Q8L3vpdEY6O57hlJkiCKIoLBYLV3xRHEYjFuJn0bNmzA\nb37zGzzyyCOGb5soGRKLToGtHPPAyEmrmVFVFS0tLekaGDsIDj2yLKOtrQ3dunWr9q4YgtZoSFEU\nhEIh+Hw+W4wZicX8wuYfO/6Bu/91NzY2bcS1k6/FwrELEfAEoCjAb37jxT33+HD77UlccIHk6NS7\ncsSiqgItLZ31edt2SNi8qwlf7oli58EmNCWakHQ3IeU+iJS7CSl3FKI7ipS7GQmhCUlXMyRPM+Bt\nhyCG4ZHr4Ffr0CNci0FHRNCzNoJafy3C3jAi/gjCvjBqfbVpocQEEhNNQU8QNd4a+N3GL95lqotk\nX7l6RRodtVVVFSk5hZgYQ4fUgVgqhnaxPS2eW5OtaEu1oS3VhtZkK1pTrWhJtqAl2YLmRDOaE81o\nijejVWyGW3Cje6A7uge7o0ewR/rnhmADetb0RENNA3oGe6JnTU+4473xl8d74rcP+XDCCTIWLRJx\n9NEyzJCEQmKxsrS3t3Mr21i5ciVee+013HPPPYZvmygZEotOgadYbGlpQSgUsm2euaIoacEBAIFA\nAIFAwBaCQ4+iKGhpaUF9fX21d6UstGPm8XgQDAbR3t5uq0UNI+87u4pFxod7PsSy95fh33v/jWuP\nuRaLxi5C0BvEZ5+5cMklATQ2Krj33gSc2tor2zltaZXxzodR/OOTA/jo84P4fMd+tKv7IQf3QQnu\ngxrcDzV4AEL4AITQfqieGPxKd4SEHqjzdUedrx5hV3eE3T0Qdtcj5Krv/O7uhj7dumFg724YfEQE\nA3rVwuux5n2ZT0QCnfXuHo/HUIdWI/a7Q+pAU7wJB+MH0ZRoQlO8CQfiB3Cg4wAOxg9if8d+HIgf\nwL6OfdjfsR9xKY6GQC+4OnqjfU8ftO/uizpXHwzt1QfjBh+BU47phSmj+qBHsHtFj4+1UAmYNU/W\nRqiqilgsxk0svvjii9i6dStuueUWw7dNlAyJRaegtRc3mtbWVgQCgaqlMPFCb1oTCAQQj8fTjaXt\niNXFotaN1uv1IhgMpsWh3RY1nCwWAZR0D36y7xMse38ZVu9ejcWTF2PRuEVwyyHceqsfzz7rwY03\nprBwoQib3t5pOsQO7IntwZ72PdgT24Pt0R34fM8+bN1/EDtb9uJgci/asQ+y7yA8Uj0i7p7oHeqF\ngQ0N6N+tM9LUK9QTPUMN6BVqQEOoMxpV569Lp2Q6HSYi2fUqCEJaRAL82nzwJCElsK9jH/bG9mJv\nbC92tu7B2m17sHHnXmyL7sb+5C7INTvh8sXR3dsP/cL9MKShH4b06Icja4/EgNoBOLL2SPSP9EfQ\nG4SqAq2thwx9VBUYOVJBOFzcfpFYrBxMLIaLHaQCeeyxx+B2u3H55Zdz2T5REiQWnQJPsdje3m4r\nAcUMUDKZ1sRiMbjdbtu+lKxqWJRJ2OsjiCQWM6Oqavr8sclqthYFZsCItL5P93+Ku9+/G//Y+Q9c\nPelqXDr+Uny+thY//7kfa9e6cMMNKXzrW9YTjaqq4mD8IHa278Sutl3Y2b4T25t34dNte7B5727s\n7diNhG8X4E7AHe8DT+IIeOJ9kNjfByGlDwbU90Zj314YM7AnJo/shSljuqMmYI/7pVpkitpmi0Tm\navNhheexqgKbNwt45c0E3vxwN748sBO7Yrsgh75CTd9tcNVvQ4fvKyT92yEk66E2DYG7dQhCqcGo\nUwfB2zYYOz8djr61R2D8OBVjxyqYOlXGpEm5zXXMaNBkVxRFQTweR4hTz5df//rXaGxsxPz587ls\nnygJEotOQZIkyLLMZdt2EFCqqqadTXOZ1nR0dKQNUuxKU1OTZcSivkdiLjfa1tbWdJ2pHSj3ePQT\nVu3vMj3/zSIijZwYrjuwDsveX4Z3d7yLxZMW49IJl2L9JxH8/Od+rF9/SDSaJWmiJdmCHa07sKNN\n99W6Azvbd2J3+26EvCF0c/WDq70/Yrv748CW/ugT6otJw3vjpKN749ijjkDYXQ9ZFv7zBfTsmUBt\nLWyXHWIGikmbLkZEsvvQCs/paBTYtq2z52Q4DNR3lyHX7EaLsBU741uwtXkrtrVuw5bmLdjSvAUt\nyTb0EAbDHxuK9u2NaP5iOEb0aMTJY4Zi5vE9MHly1/6UJBYrB2/n2Z/+9KeYO3cuvva1r3HZPlES\nJBadAk+xaGUBpTVAEQQhnU6b7QXMWi7Y2aLb7O62mXokFlJDSmKxE+2EFEDWqIVeQJpFRPKYGK47\nsA53vX8XVu5YicWTF+PS8Zdi7cdh3HmnHxs3unD55SIWLkyBZ3Y2iwpua92Gr1q/wlctX+Gr1q+w\nvW07trd2fsmqjAG1A9A/0h+9/P1RhwEQWgegY8+RiG49EjvXD8CGtSE0Nio44QQZ06ZJmDpVRj5z\n42q7odqZRCIBt9td1nMnl4jMZa5jVdpSbdjSvAVfNn+JL5q/wPq9m/HJzi+wrX0TRFmCsn84IskR\nGFhzFMb1HY6pw4ZgxqQB6HuE9eYgVoO3mdB1112HxYsXY/z48Vy2T5QEiUWnIMsyJEnisu14PJ52\nmrQKegOUQCAAj8eT9wWbSCQgy7KljrVYzOpuy6K/pfZIbGtrg9/vt82EuNjjKVQk5qPaIpJnFOGz\n/Z/hrvfvwj93/TPtnvrFujo88IAPr7ziwYIFIq64IoWhQ0t7Bbal2rC1ZSu2tWzD1pat6Z+/av0K\nW5u/AmQffLFBQMtA+DoGwhcfCH98IPzxIyG0DkT7ge5obXGhra2zeXpDg4rGRgXDh3d+jRihYPTo\n/OJQD4lFfhghFrOhzQQoxqHVyhyMH8T6fZvx7vpNWL31c3zetAF7lY1IenfD2zYcjXUjcdoxR2Hy\ngFE4qsdRGFg3kOpoDYR3fejChQtx3333oX///ly2T5QEiUWnwFMsJpNJiKLIreDZSLS1bV6vNy0S\nC8VKx1oqZhOLqqoilUql3WhLbVlit9raQsWiUSIxH5USkZVIOVu7fy2Wvb8Mb2x7AzMGzcC5R52L\nMf6Z+NMfwvjTn7w47jgZV18tYupUuUvLDUVVsKd9D7a0dKbTfdnyJbY0b0kLww6xA4PqBmFQ3SD0\nrRkIaf9g7Fk/BJ+tHIbE3oGYMS2MGTMkDB3KzmXnF9DZiL6uTkVtrYq6OsDI0lsSi/zgKRazUWyb\nD+09aUUSiQTiUhJvrNmGP7ywEau3rUfvsZ8i1W0t2qUWjGoYhTE9x2BMzzEY23MsRjWMQsQXqfZu\nWxLeYvHMM8/ESy+9ZMlMNRtDYtEpKIoCURS5bDuVSiGZTCISMe/Dt5jatlxY4VjLxSxGMNoUYdbX\nspDobzacJBbZ81uW5fTP1ZoMZqqHzGS2VaiIrGR90sH4Qfx101/xzIZn8On+T3H6sNNx+qBz8elb\nR+GR5V/B3XMz/H02o823GTH/F4gHvoRbisDfMQT+jqEIxocgGB+KQHwwgomh8Eu94BIEJBICPvvM\nhYkTZZxyiowZMySMGaOgWpnf1RA0ToE5aFf7eQrkFpGANR1agcPP8a5dAh580IfHHvPi+Bn7MeaU\nfyM0+BNsaluLT/d/io0HN6JPuA/G9x6P8T3HY1yvcZjQewJ6BB3aO6cIeD9/Z8+ejffee8/015zD\nILHoFHiKRZYaWGuG7rwa9KY1TCSW8xAy67EaSbVr+zL1SDRiomUHIyYtmcSvmURiPkoVkdUys9jV\ntgvPfv4snt7wNPa078GQbkNRkxiKenUo+gaGoF9wKPrXDEZtIJKO+qkqoCiHIoTszx4PMGGCDLOs\nOZFY5IeZxGI29CJS/7PZRWS2cxyNAs8958ULL3jwr3+5MXWqjDPOkDBzdgJR90Z8su8TfLLvE6zZ\ntwZr9q1BfaAeE3pPwMTeEzGx90RM6D0B9QFrtpHiBc8sBFVVMWfOHBKL5oPEolNgqXw8kCQJsVgM\ndcUWynBCn7aYz7SmGMx2rDyoVm1frh6JRmBnsaid7JldJOYjl4hk5kaCIKRTkavtzmoHSCzywwpi\nMRdWaPPR0dEBv9+f833R0gL8/e8evPiiB2+84cFFF4m48cYkunXr/HtFVfBF8xf4eM/H+Hhv59ea\nfWtwRPgITD5iMiYdMQmT+0zG2J5j4XM7N12bdw3unDlzsHLlSsO3TZRF1hvamk81oiq4XC5uPRyL\nQRuRcrvdqKmpKSttMROCIGSsw7ITlT5GfY/E2tpaLvWSdhs7djwsisicEa0qEhla4ceuA5aSLIoi\nXC5XWiiy547W6Vl/DkhIEtWE3ZdWRRAEuN3uw57JehHJejmb1aG1rg4491wJ554rYc8eAT/7mQ+T\nJoVw440pLFggoUcPFxrrG9FY34gFIxcAACRFwoaDG/DB7g/wwZ4P8Mc1f8TWlq0Y12scpvSdgmP7\nHItj+x6L3qHeVTuuSsPzehZF0bKLKk6FIos2JJlMctlutRu5l2taUwyKoqClpQX1PD30q0x7e3va\nIZYnRtWRFkpHRwcA2KLtiaqqiMViUBQFHo8Hbrc7PSGzEyxLIJlMpqPC+klrKemsAIlILRRZ5Ech\nUS87kSkSyX7HS0TGYjEEg8Gi7+m1a134xS98eOstDwYNUnDSSTJmzpRw4oldjau0tCZb8eGeD7Fq\n9yqs2rUKq3evRn2gHlP7TcXUflNxXL/jMKx+mKUXCHLBM1K+d+9e3HTTTVi+fLnh2ybEjwddAAAg\nAElEQVTKgiKLToJXZKVaD0W92OAVkdLCzqHVV4tzwfO4MvVIDIVCFTmXdogsagWRx+OBJEmQJAnJ\nZDKdFsaEo1ZAWu1aZZHEVCoFj8eDUCiU9d7OFIkEMotIrZBk0UgSkQRhHLkikVohKctyOhpZrUjk\nmDEK/vd/ExBF4MMP3XjrLTd+8IPOWuhrrknh3HMl6Ksxav21mD5wOqYPnA6gM33186bP8Y+d/8B7\nO97DPf+6BzExhqn9puL4/sdjWv9pGNNzjG3ad/Cc+7CgA2EdKLJoQ5gxBA+i0WhFxBoTG/F4PG3f\n7Pf7KzrBa2pqqloUtRJ0dHRAEARDravL7ZFoBFbukVlI+wuWksomYux7JhHpdrtNma6qKApSqVRa\nJPKIyGQTkfpno5NEJEUW+VFq1Msp5GvzkavVB6O9vd2wRUdVBV5/3Y377vNh0yYXLr9cxMknSxg5\nUkGhnlo723Zi5Y6VWLljJd7b8R72d+zH1H5TccKAE3DSkSdhdMNoy4pHntfzypUr8dprr+Gee+4x\nfNtEWVBk0UnwjKy4XC6uURuepjXFws6j2SbaRmHkdWJUj0SnUkyPREEQMqYG6UVkKpU6TERqhWQ1\nRKReJOaKJJYLRSIJwjxkM6nKJCIlScrY5gPovH+NiEYKAjBjhowZM+L4979d+MMfvHjyyQC2bHFh\nxAgFEybIOPtsCSefLGdtddMv0g8LRi5I1z7uje3Fyh0r8e72d/HImkfQFG/CCQNOwIkDTsTJR55s\nqbRV3pHFHj2ofYmVoMiiDWEpHzzg1W5BVdW0Q6bL5UIgEKi62DBb03qjMSICZ3SPRCNgBinhcLhq\n+1AoxYjEcj4jWyRSn8rKS0QyUypRFNPOrmYUX9q6KztGIimyyA+KLBqPPp2VOSTzdGjt6OiscVy9\n2o3HH/eio0PAJZekcP75IorVN7vaduGd7e/g7e1v461tb0EQBJx85MmYPnA6Tj7yZPSs6VnWvvKC\n1crzKh157LHH4Ha7cfnllxu+baIsqHWGk5AkqYtroJEY3W5B30aBp2lNsZilaT0vWD1hKaKKV49E\nI2BGKRGzNLfLQCVEYiH7wFtEWkUk5sMuItLq7R3MjJEpksThKIqCeDyOUChUUJsPfVprKeOiqsCq\nVS78/vc+vPSSB5Mnyzj9dAmnnSahb9/ipseqqmJzdDPe2PYG3vzqTazcsRKD6wbjlEGnYMagGTi2\nz7Hwus2xiMPEIq8F1/vuuw/Dhw/H/PnzuWyfKBlKQyWMQWtjXw5a0xqebRTKwQ5GKbko5eWpF/dm\nHDczYwaRyCg0nZUtPhUjIvUiMRwOm1I8FQrb90wOrZTOShCVpdA2HyydtdQ2H4IATJmiYMqUBGIx\n4PXXO/s33nGHH4MHKzjtNAmzZ0sYM0bJ6qqq3efG7o1o7N6IyydeDlEWsXr3ary29TXc8tYt2NKy\nBSf0PwEzB8/EzMEz0TfS14hTVRK8y2+i0SgaGhq4bZ8wHoos2hCekcVyTFEyOWSaOdJQrab1laKY\nCJy+R2Km1gZmgRns1NbWVntX0phJJJaKNh1M+10rIl0uV1pgskwBs97fPDFrJJIii3zgnbZHdL6D\nkslkSS2R8pnrFCsiRRFYudKNFSs8WLHCA1EEZs+WMGuWhJNOklGKZ9y+2D68vu11vLrlVby+9XUc\nWXskZg6eiVlDZmHyEZPhdlXufVvOuS6E6667DosXL8b48eO5bJ8oGUpDdRJsssYD5nJZzENEa36i\nqiqCwWDVTGuKob29PZ06Z0cKEVWV7pFoBGYSi3YQiflgK/jJZDI9+QJQ0ZpIq1BtEUlikQ+80/YI\nPgKmGBHJ/qx/fqkqsGmTCy+/3CkeP/vMjTPOEHHeeRKOPz67OU4uJEXC6t2r8cqXr+CVLa9gX8c+\nzBw8E3OHzMX0gdMR9vG9ziRJgiiKhjqla1m4cCHuu+8+9O/fn8v2iZIhsegkeIrFYkxR9OYnZjCt\nKYZYLJY2bbEjkiQhFouhrq6uy+8zRYADgYBlxi3bcVUK9ky1u0gEDk3gJEmCz+fr0iYlXyRSLyTt\neo4KoVIiksQiH0gs8oe3gNGSS0QCyBqJFAQBu3cLePppD5580ouWFgELFnQKxxEjSi/f2dayDSu+\nXIEVX67AB7s/wL0z7sX8o/jV+4mimG5ZxoMzzzwTL730km3nVhaGxKKTUBQFoihy2TZroJ0rddHM\npjXF0NHRAQDcUjGqjSzLaGtrQ7du3QCYo0eiEeiPq1KwZymr7wOcKRLzkU1EAjgsCkkiMrOI1NYU\nFSMiSSzygcQif0RRhCRJVRUYWhGpF5OZHFrXrfPgqad8eOYZL0aPVvCLXyQxfHh5ng+tyVbIqoz6\nAL+m9rzF4uzZs/Hee+859rluYsjghjCGXH0WZVlGPB43tWlNMRhl5mN2qEdieegnEIC9RSLLLvD7\n/QgGg0UfJ5tIaQWL9hwy8ahtAZRJRJo9HdoIijXWYSKSTVzJWKcy2Lkfr5mo9jnO1isSONxcRxRF\nDB2axC23tOOmm1z4059CmDWrBvPnp/CDHyRRX1/aO6LWz7+8guf1bGfTQDtDYtGG8Hyg6h1CM6Us\n1tTU2GJiYnc3VKBz0tnS0gKXy4Wampqq90g0gkqNW6ZJul1FIqtJZCKxpqbG0OPUTsIKEZGyLKf/\nfxKRh8glItnfs3NHIpKwEmYX5PkcWq+6KoVzz03i5z+vwYQJEfTuLaOmRkVNDRAKAaGQim7dgDPP\nlDB9ulJSraNRVOJcm3ksicMhsUgUBZuI601rAoEAwuGwrR4AuaKoVkbbIxEAwuEwpaUVgX4yTiKR\nH/lEpDaVlURkZhGpqmrayZhNZvUtPigSSRB80IrI/v2BBx6QsHSpjAMHgPZ2Fe3tKmIxIBYDdu8W\nsGRJAC0tLnzzm3F885spDBhwKBujUs9e9jzggSiKNN+wIDRiNoT3A0UbjbJzyqLdIov6WtJIJILW\n1lZLpwpngte4ZRKJdp1Qs2wBRVHS2QJmusezpYMVKyKZO6sdYQt6yWQSHo8H4XC46D6RJCILw+xR\nLztgp3N8xBEqjjiC/anrMV1/fRwffyzgsce8OPnkGjz5ZAsmTDjkNF1sm49S4Hmuo9EounfvzmXb\nBD9ILNoUoyfMWqEBAKFQCF6v17DtmxG7iEV9j0RtLSk7Rru8hLUYdVyZ2l/YccLMRBbLFvD7/ZZb\nCCpXROpbfFgRvUgMhUJZF4SKTWcFSEQSBE8EQcDRRwNHHy3iZz8T4fd74HZ7DnNoZc8wJiIzCUkz\nZrxEo1HU1/Mz5yH4QGKRyEkmoWHHaFQmrC4W9T0S6+rqHDGhM+rl6IQeicChuuNkMmlZkZiPQkWk\nJEld6vqy9Yk0I1qR6Ha7c4rEfJCIJMwGz9RIs6I1Ys/3DNOa60iSlP59rjYf2eC5gHzw4EGKLFoQ\nEos2pVyhI4pi2rRGLzSsLqIKxYrHmclwKBQKZX3wW/EYC6GciCmJRPsdazbsICKNFIn5IBGZGbtm\nZxDmp1iH1mxtPrT3J+801B49enDZNsEPEotEGtZnT1urlMm0hrWUsHt00UpCio2dtkdiIYZDVjpG\n3jhNJDKDI9YH1Y7HWirFiEj2c6VFpPZ57Xa7027G1aAcEcnOsx1FJGEcJMiLJ59DazYRyZ4tPOoi\nqWbRmpBYtCnF3NiqqqbdMQVByGtaY1eX0GyY+SWldaUFiu+RaFexWMxxOUkkiqKIZDIJQRBIJJZA\nISJSlmWuItJMIjEfpYpI7b8nEUkA5n4PW41cIpKVHgFIZ1RoF3XKNdeJRqMYPny4YcdCVAZzvmGI\niqBtocCMEAqZPNpVYOipREpGqWgFfjk9Eu06loUcF4lE+x1rtdCKSK3xl96QohwRqR9HM4vEfNhN\nRJrxHUEQxcKeSQDg9/vTv89nrlOMiIxGo2hoaKjI8RTD008/jVtvvRUbNmzA6tWrcfTRR1d7l0yF\nNd80RF5yvbhyuWMWum07CoxMmO1Y9QKfeiQWj1NFYjAYNLVBix3RruAXKyK1/SFlWUYqlUqPo13v\nebuJSMI4SJBXhkznuVBznUwicteuXXj11VcxYsQIjBw5Ek1NTaZMQx07diyWL1+Oyy+/vNq7Ykrs\n+cYhMiJJEuLxeEbTmmJgNYtOwCxiUd8jsViBnw2zHJ/R6I+L/ewkkciiznYWF1alUBGZSqXSYohN\nvlhqGBOTdryG9ZCIJIjKUIwoL0REJhIJrF27FsuXL8fGjRshiiI+/fRTTJgwASNHjsSoUaMwatQo\nDBgwoKrPsqOOOqpqn20FaAZhU9hNV6hpTTGwlW4nUG0xVW4UOB/VPj7esGNjZhqAvUWi1hXTymmK\nToVNvJjpBEs3dbvd6ckXi0Qmk52Nuln0UZ/SasdrXI9ZRCRFvfhD57gyGHGetSJy9OjReOCBBwB0\n3pdnnXUWfvjDH+KLL77A+vXr8dJLL2HdunVobW3FyJEj8fjjj6OxsdGIQyEMhGYSNkVVVSQSibRp\nTSAQgM/nM+Rha3eBoaVax1qpHol2HUsW/SaRSFiFQlxqC0lnJRFpHhFJGIMd31Fmhee5drlcEEUR\np556KmbOnNnl75qbm7F+/Xr069eP2+efeuqp2LNnz2G/v/POO3HGGWdw+1w7QDMKm8IiioWa1hSD\nXQVGJip5rMX2SDQCu40lmwACQEdHR3qC7PF4DLcArzaV7K9H8EPf77IYA6J86aysDpLVrpKIJBFp\nZZxwjZoBnu1+stGtWzdMnTqVy+cy/v73v3Pdvp0hsWhT3G43IpEIl21TzaKxlNoj0cjPtzr6iV4g\nEOjSRyqVSqV/zjRRttJkmTnhplKptIsxiUTrUY5IzEe+/mokIrtSrohkhh7sPBLGYod3lFWoRLqv\n2Z8pdL0dDolFm8LzZnRSn0WeYrHcHolGYPaHdj70EzltsX2mSZt2sqw1EFFVNWsbA7OcIxKJ9oFl\nEKiqCr/fX7H7vlQRaeXFlXLIJyKZ+6MkSfB6vennivbfUyTSGJxwvZkBnmJRFEXTlkgsX74cixcv\nxoEDB3Daaadh4sSJWLFiRbV3yzSYc9QIQ+AldOyWupgLHsdqVI9EI7DqWOYSibnI14xYb//NRGSm\nyXKlYJFREonWp1oiMR+Fikg7RejLQRCELvdkJBJJGxNROqvxkLlN5VBVlds1GY1GTdk2AwDmzZuH\nefPmVXs3TAuJRaJomMBwwgPcyJRbM/ZItJpYzNQj0YgXmyAIGcdCax7CIi6yLKc/Vy8kjbwf9CIx\nHA7TxNKisHRTWZYRCARMIxLzQSKyK9o64UwLN1QTSVgdnvOBpqYm1NfXc9s+wQ8SizaGZ2QRcMZq\nnxHnkFePRCOwiljMJBIrce2xia5WSLLJHpsos753TERqJ8ql1H2xRQVRFOH1ekkkWhi9SKypqbHF\nM7MYEcnSvK0sIrUtqEoxkyIRWR5OmGuYCV7nuqmpCT169OCybYIvJBaJknBK3WI5Yop3j0SjMPM4\nVksk5iJfI2JWt1RsGwMSifaB3fuyLMPv99tGJOaj0DRvq4hIrUM163lpZDYIiUjCbPAU5mZOQyVy\nQ2LRxlDLhfIp5Tgr1SPRCMwwIcuEGUViPrQiMlcvvEwOlGwy7fV6qSbRwjhVJOYjW5p3MSKy0oZT\n2vpSI51qC4FEZFcoslg5SCwSmSCxSJQEicWuVKNHohGYbRytKBLzka0XHos8SpKU/ntJkiCKYtZ6\nSKufC7tCIrE0yhGRvO4Ns5oQAeWJSGbWZScRSRgPb7E4fPhwLtsm+EJi0cbwbp/hhF6L+cRUtXsk\nlotZxKIdRWI2ZFlOi0Sfz4dgMNhl4qafKEuSlLG9hzaV1a7nyuxox5JEonEUKiKz3RuliEit4LeS\nCRFQvojUOjybUURSZLEy8J4LRKNRNDQ0cP0Mgg8kFomSMIvI4E224zRDj0QjqOY4ss91qkiMRCIZ\nj7UYZ1Z23rLVfRF8KHQsCWPhISKZAZkdBX8xIpKJR72IzFajXUlILFYWSkMl9JBYtDFUs1g++jYh\nZuqRaCSVfBmz64ZN5gASiYWQy5mVTZJZTWQmZ1Ye7T2chlZYkEg0D4WKSG3/VCZ+FEVJ1wqbxViH\nN0ZEIs0gIglj4T0PiEaj5IZqUUgsEiXhJLEIHOp5Z6YeiUZQyYmRE0Wito4tGAwafqzaCVu+9h7s\nZ20NZTZnVqIrJBKtSSYRqapq2qWa1RErioJYLGZIOquVMauI5NkonjgEiUUiG9af7RJZ4V2zKIoi\nt+2bBfZCbG1tNV2PRKNgwp/X9aKdXDhBJGp761UrrS1Xew9tOmu29h5ma2FQLbTtTHw+H7UzsTAs\nKySVSsHj8SASiRw2ltlSvUlEmlNEEsbCWyymUikEAgFu2yf4QWKRKAm7Rxa1PRIBIBwOd3GytBO8\nxlI/iWCTBbtOrswgEvORzZk1UzN1NnGudguDakAi0T6w+vJkMgm3252zNU2mVG8gv4jMFKW38/3B\nqJSIpJpF62Pn+aITILFIlIRdxWKmHoltbW22flEZPZaZRKJdJ9os1TORSEBRFAQCAVOKxHxoRaQW\nfT2ktoWBHSMtWpHo9XpJJFoY5lSdSCTyisR8FCsi2b8hEUmRSCtRCVHuhOvfjpBYtDFkcFMY+Xok\n2ulYM2HU8TlNJLJIohn7sRlFLhGZzTgkU6TF7NcBiUT7oH2eC4KQNiHjQSGmU+RcfIhSRCSrt9a+\nj+38bqkmPMWiKIq28HlwKjRyNoeX0LFDn8VCeyTaXSwC5aWIZOqRaNcXuVNEYj6Kae/BJnrZmqlX\nE5Zym0qlSCTaACYS2fO8Gk7V+UynsjkXk4jsKiK1RkQejyd9LikSyQ+eYpHaZlgbEotESVhZQBXb\nI9HKx1oIpb4cMonEak/+eUEisTByRVq0zqxswqxv71EpZ1at2QmJROujNWoy671ZqHOx00WktsY0\nlxGR3jSNRGT58HSdbWpqQn19PZdtE/whsWhzeAsdKxWel9oj0QlisZjjc6JIZAsL1YpWWJlynVmN\nbO+hd8QkkWht9O1pfD6f5e7NXPdHMSLSDJH6ctA+a10uV14jIiB/Oiv7HUAisto0NTVR2wwLQ2KR\nKAn2oLWCWGT1SKX2SCSx2InTRKIoikgmkxAEgUQiB/I5s2onyFoRmSnKkm9c9CKxHLMTovpo+16a\n1Xm4XEoVkdmMp8yMPn24VOdxEpHlQWmoRDZILNoc3r0W2QTOjLAJRTKZLKtHoiAIlq/PzEU+sUgi\nkURiJSmmvQdzZs1VD6lNaSORaG30LU0ikYjj7s1CRWSudG+ziEhtZJiJRB77lE9Eag11nCwiSSwS\n2SCxSJSMWSNu2h6JPp+vZJHIqPYLtRJkGkcni8RgMGiKyRRxiEKdWZl7IrumBUGA1+tNT0StkA1B\ndIVqTPNjJRGpFf3VjAxnu4a0ItJJLT54i8Xhw4dz2TbBHxKLNsdJ7TMy9Ug04gHutMii00SitmF3\nMBgke2+LoXVmZeMpyzLcbjd8Pl/6ema9MIHD2xfQwoA50ZudkEgsnmJEJPuZl4i0iuh3qojkLRYb\nGhq4bJvgD82KiJIxg1jM1yPRCMxwnDwRBCEdiXGqSOTZi43gj348s6Wb2rHey44UOp5E6RRjPFWu\niGSZG1rfACuJKEYuEcm+W1VE8p7jUBqqtaHZkc2pRM1iNSi0R6IR2FkssuOSJAnxeLzLJMCOkEi0\nF9pJaCHjWU6UxWhnVuJwtOngWsdqonIUajxViIgEDmX8CIJg2/Fkz5NMLT7Yd6uISJ6RRXJDtS72\nu2uJilENEVVsj0QjcLlcthOL2hcXS+NjtSyZXCfZ6rFVJ8gUqbAXxYrEfJTb3qMYZ1bicLQZIqxm\n2I6iwsqUIiIZHo8nbRTmpJphK4lI3uNCYtHa0NPY5vCuWaxUZLHUHolGYKfIotY+nL0c3G73YU2i\ntWl6WtfJTBGWaq+E5oJaJtgLvRER70hFMc6sdl1o4Y2+bQK5D1sL/T0iy3J6QcXv96czkNi7hGcf\nVatQioiUJCk9F+EhInmLxVQqhUAgwG37BF9ILBIlUwkRVW6PRCOwg1jMJBKzTWC1hiFatKvHuWq9\nzPDiJ5FoLzK51VYz8lSoM6t+oSVTrZdTJsh6KtU2gagM+rYmtbW1Gcez0Gg9ichDVCISyVMsWn3+\nRJBYtD1WrVk0qkeikVgxfSaTSCx1JZK9yPVRSDZBNkOaHovykEi0B1ZraZJtoUV7jyiKAlEU0/el\n1aL15aIVidVsm0AYQ7EOp4Wms7L7nkSktdJZc+GU8bIjJBYdAK/IGI/tGt0j0QjYQ9ZKYjGTsymP\nl4T2BVRoA3UeERbtqraZLdmJwtDXsFk9PZGJSL2Q1E6OmYhk0Xr9QouZRXIhsAVASZLg8/lIJFoc\nfd1wuQtzhaZ8k4g8hJEikuf8RhRFqkG2ODR6RMkYKRZ59Ug0Cqukopql/UWhaXoswgKgpMkxiUR7\noRWJACwvEvORL1qfr4m6FSbH+vTESCRi6v0lcqNfyKlk3bB+P0hEZqZYEcnGVBAEiKLYpUzFiPcp\ntc2wPiQWHYBZI4uV6JFoFGYXi2YRifnIlKZXyORY/9JnqU8kEu0BexYkk0nHG52U68xqlslxsemJ\nhPmRZblLu6pq3qOlishMKd9Oec7oRSRzCWdlGyyimykSCaBkEdnU1IT6+nqjDoOoAiQWiZJhAqrY\n9AVt+oqiKFx7JBqFWcWiVURiLgqdHGtf+gDSqa9MfFopTZjohERi4ZSaplfpybG2TY2VG7ATh9Cm\nEPv9fvh8PtPeo4WKyFwOxk4QkWwO5nK5sqYQF5LOCuQXkU1NTdQ2w+KQWHQAvB54xea6V6NHolGY\nTSzaQSTmQx9VZC8sn88Hj8eTjkZmq4d0glmIldG2TPD7/ZZ5FpiNQibH+vskW8p3Oeff6Bo2ovrY\nKYWYRGQnzBeCLdTnWpwrpyYSODQvoTRU60NikSiLQkRUNXskGoVZxKITRKIW1rOLmWLkmqzkMgvJ\nZqpDVB4SiZWh0Lph1kQ922JLvmdMpXtfEvzRRoftnkJczmKLlUSkVviXGx0uRkTu2bMHDz74II4+\n+mjK/rEw9ER3ADxvzlwiygw9Eo2i2mKRRGL+Fe1CzULYz9Vo7eFkWLop9dWrLtnae2RabNGbT2nv\nFwBdjE6q3fuSKB+KDh+i0MUWs4vISgp/rYhMJBJ44IEHsGLFCvz4xz/GzJkz6XlvYejJTpRFpl6L\nZuyRWC7VEIvs85wmErU92ILBYFnHm68eMlfqETVPNwa9SKSWCeakkMUWVjusTTXTtgShyIF1YSKR\nosO5ybbYUoyIrMQ7RWsgmKsu0WgURcELL7yAX/7yl7jooovw9ttvd6mxJqwJPQ0cQKUii2bskWgU\nlRSL2vPJfra7WNEKiko06i62tUem5umUypobar5uffSLLWxMAcDv96cXC9nk2KzOrER2iqlhI7JT\njog0emFSP6aVEGuqqmLt2rVYsmQJRowYgZdffplMbWyEkGcCXP0iLaJsWEoRD2KxGARBSH+G3+9H\nIBCwXX0Dm/SGQiFun6HvewQ4TySa1WVPm6KnffHr6yFpYny4SDTrmBKFo00LzzWmegdjdq9Q2rf5\nsJLDqR3Ri0j2XV87XIyINLIusRj279+P22+/Hbt378ayZcswevRo7p9JcCHrxUJi0QGwnHWjtylJ\nEmKxGBRFQTAYRCAQsO3Lhj2Aw+Gw4dvWi0R2Du16LgHriMRcaFP09C99M9au8IZEov3QCgqfzwe/\n31/SmOrTvvUistIpek5GVVUkEom0w2mpY0rwoRQRCaBLXWKl5mKpVAq//e1v8eyzz2LJkiU4/fTT\n6VqyNlkHj9JQiaLQ90hkaRfBYLDKe8YXHmmoWoHIRKKdJ0nsJah1wrRyaqI2RS9X3zu7t/bQR52s\nPKZEJ/qWCeWaYpRiFlJqdIXIDPW/tAaFprNqSyTYv2N9h7W/44GqqnjllVdw1113YcGCBXj33Xfh\n8/m4fBZhDkgsOgAjHhjZeiSmUiluKa5mwkixmEkk2vmlrW+8bvd2CfkmxrncJq3U2qMUx1rC3LA2\nR6lUqiItE/JNjAtxZrXDggtPyOHUHujvFVmWEY/HoSgK/H4/gEOLPNo6e6MXXNavX4+lS5diwIAB\neOGFF9CrV6+yj40wPyQWHUKpYidfj8Rqt5SoFEYcZ6b2F3ae5DhNJOaDvewLbe2hFZ1mMgrRpyaS\nSLQ+Zos65bpXtPWQ1Es1N8wNEwA5nNoE7fM3VwuibK1wShWRTU1NuPPOO7F582YsW7YM48ePd/z9\n5SSoZtEhpFKposSOvkdith5aoiiio6MDdXV1Ru6u6ZBlGW1tbejWrVvR/9ZpPRK1lt0AyGGvBPIZ\nhVSjxsuo+jXCPOijToFAwHJRp0ztPfQLLk4zoNLWD1NPU3ugj/qXWpeoF5HsOxORH330Ef79739j\n1KhRGD16NLp3744//elPePzxx3HzzTfjnHPOsfUit8OhmkWnU2hkrNgeiS6XiyKLWXCiSBRFEclk\nEoIgkEgsA21UUV8PmavGi0d6ntH1a0T10d+rVo465eulyu4VluVg5/YeeodTqh+2PkanEWfqpwoc\nEpGqqmLjxo14/vnnsWHDBqRSKfTs2ROnnnoqdu/ejbfeegujR49Gr1696NpyEBRZdAjamo9M6Hsk\nFrrCrCgKWlpaUF9fb+Tumg5VVRGNRlFfX5/3Ael0kej3+0kkVphMq8XltvbQi0Sfz0ci0eJoo/5O\nvVeLcWa1iouxNupEUX/7wO5VVVWzZnfxYNOmTVi6dCnq6+tx/fXX48CBA1i3bh0+++yz9JfL5cL4\n8ePx97//nd4L9oEii04n24uDPYxYX566urqibnwWcdO2fLAjhRyb00UiRRKrR6bVYn1rj2yRFf2k\nWCsSK2FyQlQG7cTTyfdqLgMq7UKLFZxZzVZrShhDoXWJRtPS0oK77roLa9aswSle7VwAACAASURB\nVF133YXJkyenP/eUU05J/3+qqmLPnj344osv6HpzCBRZdAjMOAPourrMHkbl9OVpamoqKOJmdaLR\naEYx7VSRyEyPWBTazsdsJzJFVtikmC3+uN1u+Hy+tKCgsbUuVL9WHtnqIXmmfheyT+wdrn0GE9am\nWhFiSZLw5z//GY8++iiuv/56fOMb3yAR6Ewoskgc3iMxEAggHA6X/TByuVxQFMX2Lyt93aITRSJb\nxXa73Zauc3Iy+sgK6wXJxtXtdh/WKiebqQ5hXqj/pTFka++RyW2SpX7zvF/0EWJtTTNhTbRzs0pG\niFVVxbvvvovbb78dM2fOxNtvv42amhrun0tYD5rpOQRRFNHW1gbgUI9Eo15eTmqfwVL4SCTSo8Pq\n6N31IpFIxqh5pmbQ2npIu5mEWB19rSm1NuFDvtTvbPdLqe09KEJsT6rV3mTLli348Y9/jGAwiCee\neAJHHnlkRT6XsCY043MImXokGoUTxCJL0UulUmnB6DSRSM2c7YFWJOZbxS7UaZLVrlaztYfToVrT\n6pPrftHXDzNBmc+ZVTuuFCG2D9WqS2xra8M999yDVatW4c4778Rxxx1H1xORF6pZdAgsTYYHbW1t\n6fx6u8HuD2Z4kG2V2E5RFb2Y8Pv9JBJtQCXGVW8Swn7Wm4RUsr7L7ugjxH6/n86rRcjXTxXofHdr\n71c7vGOcTLXqEmVZxuOPP47f//73uPrqq/Gtb32LnhOEHqpZJPhhx16LbCWYGRkIgpB+sOdzmbRq\nVEUvJiiSaA/0jok8xzWX06R2MmxUap6TqeS4EnzI1E+VPYdZRofP54OiKOjo6ICqqoctuFjpHeNk\nqlmX+P777+PWW2/FiSeeiDfeeAORSIT75xL2gsSiQ+D5IrFTGqpWIDKRqH8Ra1ON9A3Tc1mvm9Ug\nhBmckEi0F2YSE8wkJFd9V7bUPCv1u6sERjfpJsyBvgdmOBzOuujC3jPsnjFzew+ienWJO3bswNKl\nS6EoCh599FEMGTKkIp9L2A9KQ3UIbOLIg3g8DlVVLe2ilU0kGkGmNCO9QUg1JsR6kRgIBCgtxQbo\na02tZqtfSNN0J06I9WKC9UokrE+5PTD1zqzsO3C4kzGlf1eOatUlxmIx3HvvvXj77bdxxx134KST\nTnLEM5Iom6wXCYlFB5FMJrlslz0Mw+Ewl+3zhKdILORztSKyUrVdeiMMqnGyB1YXifkopt+dmSL3\n5cJEYjKZLFlMEOaEp8OptpQi20IlpX/zoVp1iYqi4Omnn8aDDz6Iyy67DN/+9rdt9Q4guEM1iwS/\ndFEr1ixm6pFYScGUqVaF7VchtV2lGOqQW6I90acl2rW1SSH97nK1KrCiCVW5ESfCnOjbm/BwONWW\nSxSa/k3tcMqjmnWJH374IX7yk59g8uTJeO2111BXV8f9cwnnQJFFB5FKpbiIOlEUEY/HUVtba/i2\njSaTSDT7i1BvqKNNMyrEUIciifZELxL9fr8tRWIpFHPPmLEeknrq2RMzO9fqs1309wzVEOdGkiTE\n4/GKp4jv2bMHP/nJT9De3o5ly5ahsbGxIp9L2BJKQyU6RR0TSUYiSRJisZipV7KsKBLzUUibAvZ7\nlgpjlokJUTpMJCaTSapdK5JM9ZBmau0hyzKSySQkSYLf74fP57P8c4o4POJkpXZEhdQQm3nhhTfa\nhZ1gMFix6H88Hsf999+PV155BT/96U8xY8YMR513gguUhkrwQxAELiLUCOwoEhnZ2hSw1DVRFNMv\nb9YjspqGOkR56EUim5gQhVNMaw+9QQjP2i59WmIkEqH70gboTYmsmCKe657J5f5td2dWVVXT71le\nqcSZUBQFzz//PO69915cfPHFeOeddyx3TRHWg64wB8HrQWbGmkU7i8RsaKMSPp8PoVAofcz6FKNs\nL3ZyyzMfmUQimVEYS7GtPYyq7aI6Yvti93rTfAsv7F3DFl4yGVFZ8V2jb0lUybrENWvWYMmSJRgz\nZgxeeeUVdO/enfvnEgRAYpEwEOYmWu19cLpIzBSVqIahDlEe2Vol0BhUBq1BiBb9wgsT8oXWELNt\nsNq1Sk44Cf5Uq12CWSjEiEr/rqlE9N4IWCqxIAgV7W+6b98+3Hbbbdi/fz/uv/9+jBw5siKfSxAM\nqll0EKyJLw+i0Sjq6uqqNuFxqkhktRJG1jeVa6hDlIdWJAIgkWgR8tUQs/uG9TdlBidWqV0jcqNP\nJa5UuwQro4/e52rvUc0FS/auVRSlos/jZDKJhx56CM8//zyWLl2KuXPn2uaa2r59Oy666CLs27cP\ngiDgsssuw+LFi6u9W06HDG4IvmKxubkZ4XC4ornz7NplEzLAGSKR9VwzWiTmo9DJsN363FUK6qdn\nT7QRSFEU078302SYKB1tWqLZHE6tSr4Fy0zGOjzuG+0CQCXftYqiYMWKFbj77rtx/vnn46qrroLP\n5+P+uZVkz5492LNnDyZMmID29nZMmjQJzz33HEVNqwsZ3BD8ahaBytYtkkjsFImVKqhnZKtRydfn\njgx1ckMi0b6wCa82dc3j8Rw2GWbjT20KrIO+dU0l0xLtjjYFXF82UWgKeDn3jX4BoJJp4uvWrcOS\nJUswePBg/O1vf/v/7d15eBSF3Qfw7+Zgc5JwJhBiwp1rEwGFFxUVfemDBw8q2Nq+vFpbrX19S+vR\nir4kAblyACK2+kpRC+JR7z4ehYpoEdt6kmwSQjgFAuGGhIQke8zM+wfvDLNHTnZndma/n+fhUSMw\nk93s7vzmd2HQoEGaHFdrqampSE1NBQAkJCQgOzsbDQ0NDBZDFDOLYUTuEwiG5uZm5c5bsMgXWHKz\nPBA+QaK6BMYIPTDeH+rqcescqHORegiG1Wo1xHNL3dObASedrfboqK+LPy/aU/eucXWN/gL5upGf\n24iICMTExGh2A+D06dNYunQpDhw4gPLycthstrB5bR84cADXXXcdduzYgYSEBL1PJ5wxs0jBzSxa\nLJagZRbVAaI8RMfsF0nqjIQRA4muBuqo7wyHWn+KFhgkmtelPLc9nTAJwCejwhLw4NGrd406193X\njTzR2N8UcHnolNbVHS6XCy+88ALeeOMNPPHEE5g5c2ZY3TxtaWnB7NmzsXr1agaKIYzBIgVEMHYt\n+gsSzf4m6l2SaLZAwt+kvK5K8sw0UEddSmyULDF1j3rgVKCf285eN12VgAe7ryscqCecatm7Rpem\nO5NZ5Wni8s3uyMhIuN1ujyqYYFx3SJKETz75BCUlJbj99tuxbds2WK3WgB8nlLlcLsyaNQtz5szB\nbbfdpvfpUCdYhhpmHA5HUP7etrY2SJKEuLi4S/67OsokmpnZg8TeMNNAHQaJ5hVqgYR3CTinGfee\n9+J1Tjg1D+++RPl16+8zx7vy5VLXe+zatQtFRUVISUnB0qVLld69cCJJEu655x4MGDAAq1at0vt0\n6AJOQ6ULnE5nUMpF5Tvq8fHxvf47wnH9Bdck9Jy/XshQzaYEa70J6c9oqxK6uvnCPuKLvBevx8TE\nhPXjYSbqz9zu9CX6W+8h/3tPP3POnj2LsrIy1NbWoqysDOPHjw/p94xg+uKLL3DttdciPz9feQxK\nSkowffp0nc8srDFYpAuCFSzKF029qTkP1yBRnuRmsVhgtVoZJF6CUBuowyDRvOTeJvWuRCMHEv5W\nFAQjm2IE3hNOtRxwQsEnCIJSBSVXePRWZxn8EydOoLCwEDk5OcjNzUVWVhb+8Y9/4LXXXsNvf/tb\n3HnnnYZ+zyDTYrBIF6gHIwSS0+lEe3s7+vbt2+0/wyCRQWKw+bsjHMyBOgwSzUsdJJo929RZNkXL\nPXdacrvdaGtr44RTE9JyX6IkSWhsbMSmTZtQW1sLu92O2tpanDp1CllZWbDZbMjLy1N+ZWRkmPZ9\nhAyHwSJdEKxg0e124/z580hKSury9zJItCh3rM3+fYeirhY+96anSx6SECp9axQ43iWJVqs1bLNN\nnWXwjbraQz3hlL3i5uLdlxgTE6PZc7tv3z4UFxcjISEBpaWl6NevH3bu3ImamhqPX42NjVi/fj3u\nuOMOTc6LqBMMFukCeXR0oAmCgObmZiQnJ3f4e8I1SJQ/rOT+CN6xDk29GaijDhKN0LdG3ceSxO7z\nzkIaYRhVqA0mosDpaV9iIJ07dw4rVqzAt99+i9LSUkyaNKnTn6vGxkZERkYiMTFRk/Mj6gSDRbog\nWMGiKIpoampCv379fP5fuAeJkZGRSrkpGU9HA3VkkZGR6NOnj2nK8cKd+kKTJYmXpqthVHrsVVWX\nE/MGj/mo+xJjY2M1e+0KgoBXX30VL774In7zm9/gJz/5CctLyWg6fCPkJ2CYCdaHosVi8Vh1ATBI\njIyMRFxcHC80DU7u0YqKilKyEYIgIDo6WvmaXGLsXY7HyZLGIgeJWi/mNiv1a0fWk72q8p8PxHPg\nXU6ckJDA16WJqDPFWq4nkiQJ//znP/Hkk09i6tSp+Oyzz7hcnkyHV7EUEHIgKH/gh3uQGB8fz5I1\nE/Fek5CYmOj3QtO7HM97SboemRTqmjpgYd9acMmfBxERER7TKNVl4KIowul0drrao7ufK+p+8YiI\nCL43m4z3dOLExETNXrsHDx5EcXExIiMj8corryAzM1OT4xJpjWWoYUbOggSaJEloampShj/IH+Rm\nv+DynpAYzsMvzMg7SOzTp0+PsxHBGKhDgcHptaGvo9cOgA6H6sjUmWItSxIp+Lx7imNjYzXLFLe0\ntOCpp57CF198gWXLlmHKlCl83yAzYM8iXRDoYFG+EFaXgITDRTCDRHNTB4nB2qXXm4E6FBgcbmJs\nXS1Kl6tbJElSnl+WnJqHXjcBRFHEG2+8geeffx6//OUv8dOf/pSf+2Qm7FmkCwJ1QaQOEuU+RXks\ntfdFsFzeBcBvP5eRLtLk8ig5SGRJk7l4B4nB7GuSS1O9f368h4J4l7Kabb+dlvyVE/PxMx51Kaua\nnCl2u93KDRZ1CaqZb2CGAz37Er/99lsUFxfj3/7t37Bly5Ye7ZQmMjpmFsOM3Ft3KX9eDhDVw2y6\nesPuaslzqO/n0iLTRPpR3wQIxee3u/vtOFDHP+++plB7funSeD+/3vv0epLF5+sn9Og5wbahoQHF\nxcVwOp0oLS3FqFGjNDkukQ5YhkoX9DZY9BckBmpCnfpDXN2PEgoDQRgkmpvRgwh/N2A4UOci7wmY\nMTExhnp+qXOX+vyqb8CoX0N8/YQGdV+i1q/f1tZWPPPMM/jkk0+wePFi3HDDDXz+yewYLNJFDoej\n279Xj/UX3RkI4n0nONAYJJqbd8+pmYIIDtTxnU6s5VJuCj7vXZixsbEBe367ev14fwYxiAwO+fkF\noOmuU1EU8d5772H16tX4+c9/jvvvv5+DkShcsGeRLpL7Cjuj547E7oxWl3u5Ap2F1LJnjbTnHSSa\nsee0u68f79UEZhio470mgXtOzSfYuzB7s9rDCK0URqFnX6LdbkdhYSEKCgqwefNm9OvXL+jHJTIC\nZhbDkNPp7DBY1DNI7I3uZiG76kWRB/G43e5er0ig0OVdrsbptRf564U02kAd70yTlpkI0oZ6zYmW\nQURXOurFB9BhJp986dmXeOzYMSxatAhnz55FWVkZsrKyNDkuUYhhGSpdpM7IyYwWJHalu71cAJRp\nkwwSzYdBYu8YaaBOsDNNpC91tYeR1pyY4SaMFvTsS3Q4HHjuuefw4Ycfori4GNOnTw/b54EILEOl\njpgtSJRZLBafzII6C6m+wASg7OVyuVwhcQFMl8a7Z82M5abBpL6g9S7FU1/4eq/10HIgSKhmmigw\nvIdPGa0lQP4MUX8Oed+EcbvdymqpcOknVlP3JWpZMi6KIj766COsXLkSc+bMweeff+7xPkdEnhgs\nhiH1LkSzBYmdsVgsHr0m8l1qAJ1eAPMOsHEwSAyurm7CaHEBrA4SrVYr4uLi+Jo0Ee9Mk9GCxM50\ndhOms35if0N1jEwURbS1tWl+o0eSJOzYsQOFhYUYPXo0/vrXv2LgwIFBPy6R0bEMNQwtX74c8fHx\nyMvLQ05ODmJjY01/sSVfwKqDxM6+Z+8LYHUZnveHN/tQ9Ke+wIyMjITVamXPms56stuuO68h9eAL\nI5UjUvew79SXv358+UZmR0N1QpmefYmnTp3C4sWLceTIEZSXlyMvL0+T4xIZCHsW6aLvvvsO33zz\nDaqqqlBbWwuHw4H09HTk5+fDZrPBZrMhJSUl5D94uqOnQWJXOvvwZhZSewwSjaenvVzyBabL5dL8\nApO0wb7T7lPfyPR+HalXe4TS55CefYlOpxN//OMf8fbbb6OwsBAzZszQ/fEIlJ/97Gf46KOPMHjw\nYFRXV+t9OmR8DBapY6Io4vvvv0dlZSXsdjuqqqpw4sQJxMfHIzc3F3l5ecjPz8eYMWMM0xcU6CCx\nM/6GgXRUQmSEu79GoF6RwCyE8XX2GgKgrDGIiooyRRkeXaCeQs2+00vT3aFUWq/2cLvdaGtrC/g+\nzK5IkoSPP/4YpaWluPPOOzF37lxYrVZNjq2Vbdu2ISEhAXfffTeDRQoEBovUM5Ik4dy5c7Db7UoQ\nuXv3boiiiBEjRigZSJvNhn79+oXEB7x8t1W+Q221WnW9+OhOFpKLnXuGQaL5efed9unTx+e1BARu\ntyppTz3hlNni4PLOQl5qOXh3qXuLY2NjNc0W19XVobCwEGlpaViyZAlSUlI0Oa4eDhw4gBkzZjBY\npEBgsEiB4Xa7sWfPHo8s5NmzZ5GcnOwRQI4cOVLTO4hyJjEUgsTOdJWF5E4u//wFiXx8zMU7SJSf\nY3+/r7MyvHCbKGkk3hNOrVYrs8Q66aocvLc3YiRJQnt7uy6rTs6cOYOSkhLs3r0b5eXluPzyy03/\n2mewSAHEYJGCR5IknDp1yiMLuX//fkRERGDMmDHIy8tTgsiEhISAvXkbKUjsir9hOsxC+g69kHsS\nw+X7DweByhYHeqAOBY53b3FHNwJIX96D3dTZSHU/pL/PIu+dtlr2JbpcLqxbtw6vvPIKHnvsMcya\nNStsbkIwWKQAYrBI2pI/OOrq6lBRUQG73Y6amhq0tLQgJSXFI4C87LLLevTGrg4gAJh2IEI4ZyHD\n5TkOZ1pNv+RydP1wwqk5qG/EqF9L8mcRcOF1pn6OtVqF8fe//x1LlizBjBkz8MgjjyAmJiboxw0l\nDBYpgDp80fJdm4JCzgIVFBSgoKBA+bokSWhoaFCykO+88w7q6+thtVqRk5OjBJE5OTmIiYnx+MAR\nBAHvvPMOcnJykJGRYfoAoqvF6PIveS+k951fI5bgeWeLzf4chystp192Zzm6nNn0HgZilr12ehAE\nAW1tbXwdm4D6s0hNfh3LK6UkSUJbWxsABH21x969e1FUVITk5GS88847GDp0aMD+biLyxMwi6U7+\ngKmurobdbofdbkdtbS3a29uRnp6OnJwcOJ1OvP3220hISMDTTz+NCRMm8MJDpas7v6GehWSQGB7U\nQy9CcfplR72QAAfqdBf3YZqfekCR93Psr6c4kNn8pqYmlJeXo7KyEmVlZbjyyivD9ufrxz/+MbZu\n3YrTp09j8ODBWLRoEe699169T4uMi2WoZDxOpxPPPPMMVq1aBavViokTJ+LgwYM+Kz3Gjh0bched\nocJfGau//hM9s5DqLJOR+06pY+oVCUYLIDhQp3s44dT81H2JPR1Q1J3VHvI/RVFEdHS0x9/tdrux\nYcMGrFu3Dg8//DDuuusuZvyJAovBIhmH0+nEyy+/jJKSElx22WUoLi7G9ddfD4vFAkmS0NzcrGQg\nKysrsWvXLgiC4LPSo3///rxY8aM7WchglQ6pMUg0P3WWyWwBBAfqXHApAQQZg7r3NCIiIqADivy9\njl5//XXMnz8fY8eORU5ODgYOHIiPP/4YN910E5588knExcUF5NhE5IHBIhlHdXU1Hn30URQVFWHK\nlCnd+jOCIPis9Dhz5gySk5M9humMHDmSAxY60FkWMpDZE7ncNFRLEenShXOWKVwG6nDCaXiQS8dF\nUdS0PeDUqVPYtm0b3nvvPRw+fBiCIGD37t2Ii4uDzWbz+FzPy8sLu8E2REHAYJHCjyRJOH36tM9K\nD4vFgtGjR3t82CQmJhr2oi2YOsqeAD0fYMAg0fy4R8+/7pTgeQeRocztdqOtrY0TTk2ss77EYGtp\nacGKFSvw5ZdfYtmyZbj66quVyqL6+npUV1ejpqYG1dXVqK6uxnPPPYerr75ak3MjMjEGi0TAxZKp\nXbt2obKyEpWVlaipqUFzczMGDx7sEUBmZGSE/EWbXvyVsXaUhZQvOgRBMFy/GnWPnjvWjKyzgTr+\nprLq/brRK8tE2tGzrFgQBLz++utYu3Yt/vu//xv/+Z//yWw1kXYYLBJ1RpIkHD161CMLefDgQVit\nVmRlZSkBZE5ODmJjY3mB5Id3FlL+BUBZXRBKF7506ViKGHihOFCHE07NL5h9id059ldffYWFCxfi\nmmuuwRNPPIHExERNjk1ECgaLRD0lr/SoqanxWOnR1taGYcOGeWQhhwwZwkzK/1OvR7BarYiKivJb\ngtdRGSsvQkOfHCQ6HA6WImpEj4E66rLicOs9DSfeOzHVe32D7ciRIyguLobb7UZZWRlGjBih2bGJ\nyAODRaJAEUURhw4dQkVFhTJM5+jRo4iLi/NY6ZGVlRVWfXk9WY/gLwsZyuV3dIE6+2CxWJSbAXx+\n9BOMgTosKw4PemaMW1tb8fTTT+Ozzz7DkiVLlInnRKQbBotEwSSv9KiqqlKykHV1dXC73cjMzER+\nfr6ShRwwYICpPhTVQeKlZB+6U35npCEgZqNedcJ+tdDW24E6LCsOD959iTExMZq9lkVRxNtvv41n\nn30W999/P372s5+xKoEoNDBYJNKDIAjYu3evz0qPvn37Ii8vT8lCjho1ynC72LTaoddZFtK79I5Z\nyMBTlxVziq2xdTZQR542CYB9iSYlVwa0tbVpfjNAkiRs374dxcXFmDBhAgoLC5GcnKzJsYmoWxgs\nEoUKSZJw5swZj2E6+/btg8ViwahRozx6Ifv27RtyF2yhsGhdnYVUX/wyCxk4PSkrJuOSM8aCICjZ\nYr0H6lDgqfsSY2NjNc3mHTt2DAsXLsS5c+dQXl6OMWPGaHZsIuo2BotEoUwu/1Kv9KiurkZzczMG\nDRrkEUBmZmbqEvx4L1rv06dPyAVh/jIn6v4tZiG7Fgo3Ayj4uupX02OgDgWe+nnWujKgvb0df/jD\nH7Bp0yYsXLgQ06ZN488JUehisEhkRJIk4dixYx5ZyEOHDiEqKgpZWVlKGWtubm7QVnoYIUjsTHez\nkPLFr5G+t0BSP89a71cj7agnnPamXy0YA3Uo8PScZCuKIt5//32sWrUK99xzDx544AFNJ6wSUa8w\nWCQyC0mS0N7e7rHSY8eOHWhra0NaWppHFnLo0KG9vuA3e/DQVRYyXC56vYMHsz3PdEEwJ5z2dqAO\nBZ73kKLY2FjNHm9JklBdXY3CwkLk5ORg4cKF6N+/vybHJqJLxmCRyOxEUUR9fb1SxlpVVYWGhgbE\nxsb6rPTorP/sxIkTiI+PhyAIYRc8eGchO7roNUMW0jt4sFqtnHxpQnovW+9ooA5X5ASeemKx1n2J\nJ06cwJIlS3Ds2DGUl5cjJydHs2MTUUAwWCQKR5IkoaWlxWelh8vlQkZGBmw2m7LWQ5IkrF69GuvX\nr8dbb72FSZMmGToYCiR/ZaxGzUJyPUL48F53EgqlgN1ZkcOBOj2jZ1+iw+HAmjVr8N5776GoqAi3\n3HILny8iY2KwSEQXCYKAffv2obKyEl9++SU+/PBDHD58GJMnT0Z+fr4SQI4ZM4bDKzrQWRbS+4I3\nFB5DdYbJYrEouxLJfIy47kQ9UEcdRHKgTsf07EuUJAmbNm1CWVkZ7rrrLvzqV79Cnz59NDk2EQVF\nh28evFIgCkORkZFISUlBXV0dXn75ZcycORPz589Hv379YLfbUVFRgT/84Q/Yu3cvAPis9EhKSgr7\nizU54xEREeGRsfHOQrpcLp8spLqMNdiPozpIBKAEieH+/JmRus/YarUiLi7OMM+z+vWh5t0L6e/1\nZJSsfqCoqwOioqKQkJCgaRVIbW0tCgsLkZmZiY8++giDBg3S7NhEpD1mFonCUFVVFW688UbcfPPN\nKCoqwqhRo/z+PjnQkFd62O12VFdXo6mpCQMGDFCCR3mlB8sZ/fM3AESdNQlWFtK7DJFBojmF25Ci\nng7UMVMpq78bP1o5ffo0li1bhv3796O8vBz5+fmmeVyJiGWoRKTicrnw/fff93o5siRJOH78uMdK\nj4MHDyIqKgpjx45VspB5eXmGym5orTu9kL3JQhqxDJF6LpgTTo3IzAN19OxLdLlcePHFF/HnP/8Z\n8+bNw+233x7WP2dEJsVgkYiCS85u1NbWoqKiQlnp0draiqFDh3qUsaalpfFiowNdZSE7690SBAEO\nh6PDRetkDt79p7Gxsczqd8DoA3X07kvcsmULli1bhttuuw0PPfQQYmJiNDm2VjZt2oSHHnoIgiDg\nvvvuw7x58/Q+JSK9MFgkfdXX1+Puu+/GiRMnYLFY8Itf/AK//vWv9T4t0oAoijh8+LCSgayqqsLh\nw4cRGxuLnJwcj5UeWl4IGY2/YTrqLKQcYMoXlAzGzYmlxYER6gN1vPsStc4a7969G0VFRRg0aBCW\nLl2KIUOGaHZsrQiCgLFjx+KTTz5BWloarrzySrz++uvIzs7W+9SI9MBgkfR17NgxHDt2DJdffjla\nWlowYcIE/OUvf+GbcpiSJAnnz5/3WenhdDpx2WWXefRCDh48mBfDHZAziS6XSymrE0UxZC54KXBY\nWqwNf72QWg/UcbvdaGtr02VqcWNjI8rKylBTU4PS0lJcccUVpv05+9e//oUnn3wSmzZtAgCUlpYC\nAB5//HE9T4tIL5yGSvpKTU1FamoqACAhIQHZ2dloaGhgsBimLBYLEhISFofJuwAAGUtJREFUcNVV\nV+Gqq65Svi6KIvbv34+Kigp8/fXXeOGFF3Dq1CkkJCQgLy9PyUKOHj06rDMq3gNNEhMTPbIOHU2Q\nlHsfvYfphOvjaATqCad9+vRhD3CQya8RdYDmXRrucrngcDgCPlBHFEW0tbXpckPA7XZj/fr1ePnl\nl/Hoo49i1apVpq9OOHLkCNLT05X/HjZsGL766isdz4goNDFYJM0dOHAAFRUVmDRpkt6nQiEmIiIC\no0aNwqhRo3DnnXcCuHCh1tjYqGQgn332WezZsweSJPms9EhOTjb1hbT3QJP4+Hi/vWqdXfDK2RKn\n0+lTdud9wUv68b4hoPV6BLpInVX0tyZHHUT6G6jT1WvKuy9RyxsCkiRh27ZtWLRoEaZPn47PP/8c\nsbGxmhxbb3yPI+oeBoukqZaWFsyePRurV69GQkKC3qdDBmCxWNCvXz9cf/31uP766wFcvEiTV3p8\n+umnWL16NZqamtCvXz8lgMzPz8fw4cMNP/xD3b8UGRnZYZDYme7ssXO73R7DP5iF1J53r1pvnmvS\nhsVi8SkR9R6o4/2a8i5jdbvdys0frW8I7N+/H8XFxYiPj8ebb76JYcOGaXbsUJCWlob6+nrlv+vr\n68PuMSDqDvYskmZcLhduvfVW3HTTTXjooYf0Ph0yIUmScPLkSVRWVioDdQ4cOIDIyEiflR7x8fEh\nH/h4T73Uqn9JnYVUZ06YhQwevZ5r0oZ3Zl8OIgEoVQBa9Rc3NzdjxYoV+Prrr1FSUoLJkyeH5WvY\n7XZj7Nix2LJlC4YOHYqJEydywA2FMw64IX1JkoR77rkHAwYMwKpVq/Q+HQojconXzp07lSByx44d\naGlp8VnpMWzYsJAo9ZMDB4fDEVJTL/2t9DDKCoJQxgmn4UM9qEheeaLVQB1BEPDqq6/ixRdfxNy5\nczFnzpyQeL/T08aNG5XVGT//+c/xxBNP6H1KRHphsEj6+uKLL3DttdciPz9f+bArKSnB9OnTdT4z\nCleiKOLIkSOw2+1KFvLIkSOwWq3IyclRAsjs7GxNV3qoAwer1RryUy87ykICxl+EHmx6LlonbUmS\nhPb2drhcri53oPrbtSr/d28G6kiSpEz+vO666zBv3jwkJiYG61slImNisEhE1BV5pUd1dbUyUGfn\nzp1wOp1IT0/3WOmRkpIS0At7s61G8LfDjlnIC7wnnHK/qHmph1JFR0df0g5U74E68r8DF27MnDlz\nBlu2bEFeXh5yc3MRFxeH+vp6FBUVwWKxoKysDJmZmQH87ojIRBgsEhH1liiK+P7775Uy1qqqKpw4\nccJnpceYMWN6XEKozi51lXEwunDPQgYycKDQJw8qslgsSslpoKkH6uzduxdlZWXYsWMH9u/fj5SU\nFLS0tGDmzJmYMWMGCgoKkJGRwZ85IvKHwSIRUSBJkoSmpiYlA2m327F7926IoogRI0YgPz9fGabT\nr18/n8CnoaEBn332GWbMmBHW2SXv6ZH+spCB2GGnJ+9ptjExMZxwamJylYAoipr3oIqiiDfffBPP\nP/887rjjDgwbNgw1NTWorq5GVVUVmpqalJtbs2bNwrRp0zQ5LyIKeQwWiYi04Ha7sXv3bqUPsrq6\nGo2NjUhOTkZeXh5GjBiBiooKvPXWW5gzZw6WLl3KwMEP7yykd8mdUbKQ6uwSJ5yam7q8WOsqAUmS\n8O2332LBggWYOHEi5s+fj6SkJJ/fd+bMGdTU1KCqqgojR47ETTfdpMn5EVHIY7BIRKQXSZJw8OBB\nLF68GG+88QZsNhsSEhLgcDgwZswYj5UeCQkJIRv46E2dhVRnIjvKQupZbqdndom0pXd58dGjR1Fc\nXIz29naUlZVh1KhRmh2biEyDwSIRkR6cTifWrl2LpUuX4tprr8WiRYswZswY5QJTXukhZyFbWlqQ\nmprqMUwnPT2dfUad6CwL6T1MJ9hZyHDqQQ136t2YERERmpcXt7W14ZlnnsHmzZuxaNEi3HjjjfxZ\nI6LeYrBIRKSHJUuW4J///CeWLl2KcePGdfn7RVFEQ0ODx0qPw4cPw2q1Ijs7W+k3ys7ORkxMDC8O\nO9DdLKQcQF5qMK5ejRDOPajhQu++xL/85S9YvXo17r33XvziF79geTMRXSoGi0REehAE4ZKzDZIk\nobW1FTU1NUoAuXPnTjgcDgwbNswjC5mamsogpRP+humol6D3NAupLkGMiopCTEwMs8Ampndfot1u\nR1FREWw2GxYsWIB+/fppcmwiMj0Gi0REZiOKIg4cOKAEkHa7HcePH0d8fLzPSg+j720MJu8sZEdL\n0NVZSE44DS969yUeP34cixYtwunTp1FeXo6srCzNjk1EYYHBIpHZtbe347rrroPD4YDb7cbs2bOx\ncOFCvU+LNCZJEs6dO+ez0kMQBAwfPhw2m01Z6+FvpQdd1FkWUpIkWCwW9OnTB9HR0SE9kZV6T+++\nRIfDgf/93//FBx98gKKiItx00038OTMBSZJw7bXXYv78+Zg+fToA4K233sJLL72EjRs36nx2FKYY\nLBKFg9bWVsTFxcHtduOaa67B6tWrMWnSJL1Pi0KAIAjYs2cPKioqlGE6Z8+eRVJSkjKN1WazYdSo\nUcyQdUAQBLS1tUEURSVTq85C+itjZUmqccnPtyRJiImJQXR0tGbHFkURf/3rX7FixQr8x3/8Bx58\n8EFNj0/Bt2PHDtx5552oqKiAy+XC+PHj8be//Q3Dhw/X+9QoPDFYJAonra2tmDJlCp5//nlceeWV\nep8OhShJknD69GllmE5lZSX279+PiIgIn5UeiYmJYZvR6M6EU3/DdNS9kN4rPcL1sTQCPSfaSpKE\n2tpaFBYWYuTIkVi0aBEGDhyoybFJe/PmzUN8fDxaWlqQlJSE+fPn631KFL4YLBKFA1EUMX78eOzb\ntw+/+tWvUFJSovcpkcHIvVl1dXUeKz2am5uRkpKi9EHabDZcdtllps6cSZIEh8MBp9PZqwmnnfVC\nemchIyMjGUDqzLsvUetpw6dOncKSJUtQX1+P8vJy2Gw2zY5N+mhtbcW4ceMQExODb7/9ltlj0lOH\nb3actUxkIhEREaisrERTUxNuv/127NixA7m5uXqfFhmIxWKB1WpFQUEBCgoKlK9LkuSx0uPdd99F\nfX09rFYrsrKylCxkTk4OYmNjDR34eE84TUhI6FVQbLFYYLFYEBER4XER6J2FdLlcPllIdRmrkR9L\nI5D7Etva2hAZGYn4+HhNS7GdTideeOEFvPnmm5g/fz5mzJhh6pswdFFcXBzuuusuJCYmMlCkkMVg\nkciEkpKSMHXqVGzatInBIgWExWJBWloa0tLScPPNNwO4cJHd1taGmpoa2O12vPHGG6itrUV7ezvS\n09M9eiFTU1ND/gLYe5hJsIIGi8WCqKgoj914kiQpWUdBEOB0OiEIAiRJYhYyiNR9iXFxcZruK5Qk\nCZs3b0ZJSQlmzZqFbdu2wWq1anZ8Cg28IUShjsEikUmcOnUKUVFRSE5ORltbGzZv3ozHH39c79Mi\nE7NYLIiLi8PEiRMxceJE5euiKOLgwYNKGeuGDRtw9OhRxMXFITc3V5nIOnbs2JBZ6SEHiZIkITY2\nVvMl5+qsYkdZSEEQmIUMEHVfojy8RsvHrq6uDkVFRRgyZAjef/99pKSkaHZsIqKeYLBIZBJHjx7F\nPffco5S2/ehHP1IyQERaioiIwPDhwzF8+HDcfvvtAC4EPc3Nzco6jxdeeAG7du2CIAjIzMxUMpA2\nmw0DBgzQ7MJdEAS0t7dDEARdgoau9CYL6Z2JDKXvR2/efahaD246e/YsSkpKUFdXh+XLl+Pyyy/n\n80P8GaCQxgE3RESkG0EQsHfvXmWlR1VVlcdKD7mUVV7pEaiLKlEU4XA44HK5NJ94GSz+hukIgqBk\nHb3LWI3+/faEJElwuVxob29HZGQkYmNjNS2LdrvdWLduHTZs2IDHHnsMs2bNCvmybCIKK5yGSkRE\nxiBJEs6cOaMM07Hb7di7dy8sFgtGjx7tkYXsaWZInVmKjo6G1Wo19UW7nIX0XukRTllIPUuMJUnC\n1q1bsXjxYtxyyy149NFHERsbq9nxiYi6icEiEREZl5wZUq/0qKmpQXNzMwYOHKhkIPPz85GRkeET\nADqdTqxfvx633norkpKSEBMTY+ogsSvqMlZ1JtJMWUi9+xL37duHoqIi9O3bFyUlJUhLS9Ps2ERE\nPcRgkYiIzEeSJBw9etQjC3no0CH06dMHWVlZyM3NRXt7O9asWYOhQ4dizZo1yMjI0Pu0Q1J3spDq\nTGSoBpCXuh/zUp07dw7l5eWoqKhAaWkpJk6cGLKPVSC89dZbWLhwIerq6vDNN99g/Pjxep8SEfUc\ng0UiIgoPkiShvb0dr732GkpKStDS0oLJkyfj6NGjPis9hgwZEtYZxu7oLAvpr4xVr8BI3ZcYFRWl\nefZYEARs2LABf/rTn/DQQw/hxz/+cVj8bNXV1SEiIgIPPPAAVq5cyWCRyJg6fOPmNFQiIjKVPXv2\n4IknnsDXX3+NJUuWYM6cOYiMjIQoijh06JCSgXz11VfR0NCA2NhY5ObmIi8vDwUFBRg7dqwpBt4E\nilya6m8iqxw8+pvIqmUWUu5LBKDLvsR//OMfWLRoEW644QZ89tlnSEhI0Oz4esvKytL7FIgoiBgs\nEhGRaTQ2NuKGG27A3Llz8corr3gME4mIiEBmZiYyMzNx2223Abhwod/S0qKs9HjppZewa9cuuN1u\nZGRkeAzTGThwIAPI/6fe86imzkK63e6gZyH17ks8ePAgioqKEB0djVdffZUlzkRkOixDJSIiU3E4\nHLBarZf0dwiCgH379qGyshKVlZWoqqrC6dOn0bdvX9hsNqWUdfTo0SHdvxcKvLOQ8r8D8BmmExER\n0a3HUu++xJaWFqxcuRL/+te/sGzZMlx99dWm/hmYNm0ajh075vP1ZcuWYcaMGQCAqVOnsgyVyLjY\ns0hERHQpJEnC2bNnfVZ6AMCoUaOQl5eH/Px82Gw29O3b19TBQyD4G6bTVRYyFPoS//znP+OPf/wj\nHnzwQdx9990+2dVwxWCRyNDYs0hEFEiCIOCKK67AsGHD8MEHH+h9OqQBi8WC/v37Y+rUqZg6dSqA\ni0NVdu3ahcrKSnz88cdYuXIlmpubMWDAAI9hOsOHDw+LgSfdJfdCqnlnIR0OB0RRBHDh8RdFERaL\nBVarVdO+UkmS8M0332DBggWYPHkytmzZgr59+2pybCPpIgFBRAbEzCIRUS889dRT+O6779Dc3Iz3\n339f79OhECNJEo4fPw673Y6KigrY7XYcPHgQ0dHRyMrKUoLI3NxcxMXFMQvZCUEQ0NbWBkEQlME1\ncm+kOvuoHqYTyMfzyJEjWLBgAVwuF0pLSzFy5MiA/d1m8N577+HXv/41Tp06haSkJIwbNw4bN27U\n+7SIqGdYhkpEFCiHDx/GT3/6U8yfPx9PPfUUM4vULfJKj9raWqWMdceOHWhtbcXQoUM9hukMHTo0\n7LOQ8uPlcrn89iV6ZyHlMlYAPmWs3e2FVGttbcXq1avx6aefYvHixZg6dSqDeiIyK5ahEhEFysMP\nP4zly5fj3Llzep8KGYjFYkFsbCwmTJiACRMmKF8XRRH19fVKAPn666+joaEBMTExyMnJUXohs7Oz\nw2Klh3dfYkJCgt/A2d9EVkmSIEmSEjy63W6llNVfFtLf3yuKIt599138/ve/x3333YetW7dquoqD\niCiU8N2PiKgHPvzwQwwePBjjxo3D3//+d71Ph0wgIiICGRkZyMjIwMyZMwFcCHrOnz+PqqoqVFZW\nYv369airq4PL5fJZ6TFo0CDTBJButxttbW2wWCyIj4/v8fAYuQQ1IiIC0dHRytflAFLORLpcLgiC\ngLlz5+L06dNKWXB8fDzWrl2LCRMmYPPmzUhOTg70t0hEZCgsQyUi6oH/+Z//wYYNGxAVFYX29nac\nO3cOs2bNwssvv6z3qVEYEAQB+/fvV7KQdrsdp06dQmJios9Kj6ioKMMEkYIgoL29HaIoIiYmRpNz\nlyQJhw8fRkVFBb777jt89dVXSllwVlYWCgoKUFBQgPz8fBQUFGDgwIFBPR8iIh2xZ5GIKNC2bt2K\nFStWsGeRdCVJEhobG31WekiShJEjRyoBZH5+PpKSkkIqgFT3JWo94RQA2tvb8eyzz2Ljxo1YsGAB\nfvCDH6C1tRU7duxQgvGqqipUVVUhPj4en3/+OQfcEJEZMVgkIgq0rVu3YuXKlZyGSiFHLrvctWuX\nMo21uroa586dQ//+/X1Wemi9K1CSJDidTjgcDkRHR8NqtWo60EcURXzwwQd46qmncPfdd+OXv/yl\nR9mqv/M9ePAg0tLSOv19REQGxWCRiIgo3EmShJMnT6KyslL5deDAAURFRfms9IiPjw9Klk8eXiMP\n/NEyUJUkCTU1NSgsLERWVhYWLlyIAQMGaHZ8IqIQxWCRiIiIfEmSBIfD4bPS4/z58xgyZIgyjdVm\nsyEtLa3XGUA9+hLVTp48icWLF+Po0aMoLy9Hbm6uZscmIgpxDBaJiIio+0RRxOHDh5VeyKqqKhw5\ncsRjpYfNZkN2drbPDkS1kydPIjIyElFRUbr0JTqdTqxZswbvvvsuCgsLceutt4ZU3yYRUQhgsEhE\nRESXRl7pUV1drQSRO3fuhNPp9FnpkZSUhOeffx4rV67Ec889h1tuuUXTvkRJkvC3v/0NZWVl+OEP\nf4i5c+eiT58+mh2fiMhAGCwSERFRcIiiqKz0qKysxObNm7Fz506MHj0aV111FcaNG4f8/HzNVnrs\n3LkTRUVFSE9Px+LFizF48OCgHo+IyOAYLBIREVFw1dTU4JFHHsGhQ4ewcuVKXHXVVcoKCrvdjj17\n9kCSJIwYMcKjFzI5OTkgAeSZM2ewbNky7N27F+Xl5SgoKGDJKRFR1xgsEhERUfA89thjWLduHYqK\nijpdReF2u7F7924lC1ldXY3GxkaflR4jRozo9qRUl8uFl156Ca+99hrmzZuHO+64Q9OSVyIig2Ow\nSERERMGzefNmTJgwAf379+/xn5VXesh9kHa7Hfv370dUVBTGjBmjBJB5eXkeKz0kScKnn36KpUuX\nYubMmXj44YcRExMT6G+NiMjsGCwSERGRccgrPXbu3KkEkDU1NTh//jxSU1ORnp6O6upqZGRkoKSk\nBEOGDNH7lImIjIrBIhERGVdmZib69u2LyMhIREdH4+uvv9b7lEgnoiiioaEBmzdvRlxcHH74wx+y\nL5GI6NIwWCQiIuMaPnw4vvvuu16VOBIREVGnOgwW2f1NRESG0MXNTSIiIgowBotEZDj19fUYMWIE\nzp49CwA4e/YsRowYgUOHDul8ZhQsFosF//7v/44rrrgCa9eu1ft0iIiIwgLLUInIkJYvX469e/di\nzZo1eOCBBzBixAjMmzdP79OiIDl69CiGDBmCkydPYtq0afj973+PKVOm6H1aREREZsCeRSIyF7fb\njQkTJuDee+/Fiy++iMrKym7vZCNje/LJJ5GQkIBHH31U71MhIiIyA/YsEpG5REVFoby8HI888gie\nfvppBoom1traiubmZgDA+fPn8fHHH8Nms+l8VkRERObHYJGIDGvjxo0YOnQoqqur9T4VCqLjx49j\nypQpuPzyyzFp0iTceuut+MEPfqD3aRH12u9+9ztkZ2ejoKAAd9xxB5qamvQ+JSIiv1iGSkSGVFlZ\niTlz5mDjxo245ppr8NVXXyE1NVXv0yIi6tLmzZtx4403IiIiAo8//jgAoLS0VOezIqIwxjJUIjIP\nSZLwX//1X1i9ejXS09Pxu9/9Dr/97W/1Pi0iom6ZNm0aIiIuXIJNmjQJhw8f1vmMiIj8Y7BIRIaz\ndu1aZGZm4sYbbwQAPPjgg9i5cye2bdum85kREfXMSy+9hJtvvlnv0yAi8otlqEREREQBNm3aNBw7\ndszn68uWLcOMGTMAAEuXLsX27dvxzjvvaH16RERqXJ1BREREFCrWrVuHtWvXYsuWLYiJidH7dIgo\nvHUYLEZpeRZERERE4W7Tpk1Yvnw5tm7dykCRiEIaM4tEREREGho9ejScTif69+8PAJg8eTKee+45\nnc+KiMIYy1CJiIiIiIjIB1dnEBERERERUfcxWCQiIiIiIiIfDBaJiIjIr8bGRsyePRvZ2dnIycnB\nl19+qfcpERGRhjgNlYiIiPz6zW9+g5tvvhlvv/023G43zp8/r/cpERGRhjjghoiIiHw0NTVh3Lhx\n2L9/v96nQkREwcUBN0RERNR933//PQYNGoR7770X48ePx/3334/W1la9T4uIiDTEYJGIiIh8uN1u\nbN++HQ8++CC2b9+O+Ph4lJaW6n1aRESkIQaLRERE5GPYsGEYNmwYrrzySgDA7NmzsX37dp3PioiI\ntMRgkYiIiHykpqYiPT0du3fvBgB88sknyM3N1fmsiIhISxxwQ0RERH7Z7Xbcd999cDqdGDlyJP70\npz8hKSlJ79MiIqLA6nDADYNFIiIiIiKi8MVpqERERERERNR9DBaJiIiIiIjIB4NFIiIiIiIi8sFg\nkYiIiIiIiHxEdfH/O2x2JCIiIiIiIvNiZpGIiIiIiIh8MFgkIiIiIiIiHwwWiYiIiIiIyAeDRSIi\nIiIiIvLBYJGIiIiIiIh8MFgkIiIiIiIiH/8HdHcmi507SKAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10842d610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(xt,yt,zt, label='Kalman Filter Estimate')\n",
    "ax.plot(Xr, Yr, Zr, label='Real')\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "ax.legend()\n",
    "plt.title('Ball Trajectory estimated with Kalman Filter')\n",
    "\n",
    "# Axis equal\n",
    "max_range = np.array([Xm.max()-Xm.min(), Ym.max()-Ym.min(), Zm.max()-Zm.min()]).max() / 3.0\n",
    "mean_x = Xm.mean()\n",
    "mean_y = Ym.mean()\n",
    "mean_z = Zm.mean()\n",
    "ax.set_xlim(mean_x - max_range, mean_x + max_range)\n",
    "ax.set_ylim(mean_y - max_range, mean_y + max_range)\n",
    "ax.set_zlim(mean_z - max_range, mean_z + max_range)\n",
    "plt.savefig('Kalman-Filter-CA-Ball-Trajectory.png', dpi=150, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated Position is 0.10m away from ball position.\n"
     ]
    }
   ],
   "source": [
    "dist = np.sqrt((Xm-xt)**2 + (Ym-yt)**2 + (Zm-zt)**2)\n",
    "print('Estimated Position is %.2fm away from ball position.' % dist[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Kalman Filter is just for linear dynamic systems. The drag resistance coefficient is nonlinear with a state, but the filter can handle this until a certain amount of drag.\n",
    "\n",
    "But at this time the ball is hitting the ground, the nonlinearity is too much and the filter is providing a wrong solution. Therefore, one have to model a switch in the filter loop, which helps the filter to get it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Fragen? [@Balzer82](https://twitter.com/balzer82)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
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